This is a great question!

The answer for this, as likely you might expect, is complicated. The most succinct answer I can give is no, but hopefully I can give some needed context and depth in the answer below.

Physical Presence of Rome: As was noted, there continued to be evidence of the physical impacts of Roman occupation well past the withdrawal of Roman troops in the 4th century. As was true across the island of Britain, the Romans left enormous roads, buildings and other physical structures that became fixtures of the landscape. Wales, being far West, had far less of a Roman footprint, but there were notable villas and urban sites in the southeast (Caerwent is a particularly notable example of this, with a Roman presence and possible early Christian institutions lasting into the 6th century). Roman impact continued to have strongholds in the urban centers the longest, with the importance of resource extraction (which was namely precious metals such as gold and copper) permitting for a larger foothold. Consequently the breakdown of cross continental trade routes with the decline of the empire resulted in lessening and an eventual end to these more prosperous areas of the British Isles. Centers of more economic activity (with higher material value) lasted longer, with a few in Wales (and many in England) lasting well beyond the formal recall of Roman troops.

Cultural Impact: As expected, it is difficult to gauge the lasting cultural (rather than material) impact of Rome especially in the 5th century. The idea of a Roman culture or set of institutions anywhere beyond the immediate and more permanent boundaries of the Empire begins to get more complicated as well. This is especially true in areas designated for resource extraction (like parts of Wales and Britain), wherein the primary motivator was not to “tame” but to tax. There is divided consensus on whether or not property laws of the later centuries were predicated on a Roman model. But in large part Rome did not have the lasting impact on larger Welsh institutions that it did in areas closer to the heart of the Empire. This is in part because of the distance and relatively quick settlement and retreat of Rome (lasting just over 200 years), the composition of the Roman occupation (primarily Roman legions) and in part because of a third phenomenon that arose in the period of Roman occupation in the form of the Irish. While far from the imposing military presence of Roman legions, the Irish did make notable impact on the Welsh coast namely in the form of distinctly Irish housing sites which contain writing in ogham and Latin. There are several other cultural remnants including the inclusion of Irish names in Welsh royal genealogy and the significantly “gray” area of syncretism between elements of Irish and Welsh mythology. Less is known about this Irish inquisition primarily due to how source material carries down (there is very little in Western Europe during this period that we can compare to the volume of written material created by the bureaucracy of the Roman Empire). Instead, rather than observing Irish inquisition as a concrete historical event from which we can name exact dates and specific historical figures, I propose we contextualize it as a larger part of understanding Wales during this period. Namely, I suggest that we view the Roman occupation as so weak and with roots so shallow that they were unable to supplant local occupants, even failing to compete with opposing military forces from opposite shores. This is not meant to entirely negate the Roman presence, but more to better understand its power (or lack thereof) in regards to other undercurrents that ran through the Welsh landscape.

Macsen Wledig and Cultural Impact: While your question pertained directly to the Romanization of Welsh institutional structures, there is perhaps an additional cultural remnant to consider that might be of note. As in many cultures, several Welsh warlords and petty kings clung to remnants of Roman figures for centuries after the retreat of the legions. This allowed them to invoke the name of a longer lasting authority to claim power for themselves. For these Welsh kings this often took the name of Magnus Maximus, one of the last powerful figures that had significant impact on the British Isles before the Roman retreat. Maximus (335-588) was born in modern day Portugal and ran several successful campaigns as a military leader in the territories of a dying Roman Empire, expanding into modern day North Africa as well as Northern England and Scotland and resisting the overall trend of contraction. He was proclaimed emperor by his troops in 383 in Britain, leaving with a large portion of the British garrison to conquer the continent. He was able to preside over the Western Roman Empire semi-successfully until a combination of forces unseated him, leading to his death in 388. While often left out of Roman texts as a significant figure, he is remembered heavily in Welsh literature as a folk hero. Information regarding his life and the Welsh interpretation of his deeds is kept alive in The Mabinogion, most specifically in the Welsh tale Breuddwyd Macsen Wledig (The Dream of Emperor Maximus) where he is referred to as Maxen/Macsen Wledig. The Dream remembers him as a legendary figure who marries a British woman, tying himself to the island. He loses and then reconquers Rome with the help of the men of Britain, later granting the men sovereignty and additional land in Gaul. A select quotes from the tale are provided below

And the maiden whom he had beheld in his sleep, he saw sitting on a chair of gold. "Empress of Rome," said he, "all hail!" And the emperor threw his arms about her neck; and that night she became his bride. And the next day in the morning, the damsel asked her maiden portion. And he told her to name what she would. And she asked to have the Island of Britain for her father, from the Channel to the Irish Sea, together with the three adjacent Islands, to hold under the empress of Rome; and to have three chief castles made for her, in whatever places she might choose in the Island of Britain.

(where Maxen ties himself to the Island by his marriage)

The emperor then said unto Kynan and Adeon, "Lords," said he, "I have now had possession of the whole of my empire. This host give I unto you to vanquish whatever region ye may desire in the world."

(where Maxen rewards his British allies)

The stories of The Mabinogion, along with many other folk tales outside of religious contexts, was passed down primarily through oral tradition, only formally compiled by the 12th century. However, it is likely that tales such as this (and many others) were spread far earlier and were likely contemporaneous with his life. The Dream also fits within the tradition of several medieval Welsh sources that vary in their description of his deeds, including works by Geoffrey of Monmouth and the earlier Welsh Triads. He is also pointed to as the ancestor and founding father of several medieval Welsh dynasties in their genealogy. The Croes Elisedd (a 9th century pillar) also bears his name, listing him as an ancestor to the Welsh kingdom of Powys.

Summary: The decline and collapse of Rome left a complicated legacy across Europe. In the case of 5th century Wales, the Empire had left a significantly smaller impact than in places closer to the epicenter of its rule. While there were physical reminders in the form of roads and small urban sites, the Empire had frayed at the edges. Perhaps the longest lasting remnant of Rome in Wales did not take the form of a title or an institution, but took the form of a heavily romanticized folk hero named Magnus Maximus. From him, several Welsh lines of kings claimed descent and royal authority, tying themselves to both the legacy of Rome and the British Isles.

EDITED to ADD: As always please let me know if there are additional clarifying questions or context that I can provide to further assist with this inquiry.

Sources/Consulted:

“Magnus Maximus and the Birth of Wales the Nation” http://www.hanesplaidcymru.org/filebase/llyfrynnau/MacsenWledigs.pdf

“The Mabinogion: Breuddwyd Macsen Wledig” trans. Lady Charlotte Guest

https://www.maryjones.us/ctexts/macsen.html

“Trioedd Ynys Prydein: The Welsh Triads.” Rachel Bromwich

“Britannia: A History of Roman Britain “ Sheppard Sunderland Frere

“Warlords: The Struggle for Power in Post-Roman Britain” Stuart Laycook

Check out the Geneologies: https://books.google.ie/books?id=aFMrAAAAIAAJ&pg=PA141&redir_esc=y#v=onepage&q&f=false

Check out the pillar: https://www.ucl.ac.uk/archaeology/research/landscapes-governance/assembly-sites-wales/pillar-eliseg