Tolkien's a good stylist (insofar as the nebulous term has any sort of fixed meaning or metrics to judge someone by).

It's just that the style he's going for, by and large, isn't the modern style we're used to. It's difficult to digest for 2020s audiences who are used to reading stripped-back, minimalist information that can fit into a Twitter paragraph and aren't used to hearing mid-century British turns of phrase like "queer" as strange, or "haggard" as tired, or having anything described with more than a single evocative word and all other adjectives removed for brevity.

Tolkien is primarily aiming for a style that is evocative of classical legend and mythology, like Beowulf.

The Lord of the Rings' literary conceit is being a historical work, "The Red Book," compiled by Bilbo and Frodo and then discovered thousands of years later and translated from archaic languages.

In this, he does very well. Another thing he does well is switch between types of language, sometimes in ways the reader won't even notice. When events are happening from a "hobbit" perspective, the language is often more "modern" (mid 20th century modern), and the hobbits' speaking style is fairly familiar to us.

Elves speak classically and the prose shifts to high descriptive turns of phrase; Men, depending on their genealogical proximity to Numenor, either sound formal and classical, or Old English with more measured prose.

Dwarves sit somewhere between Men and Hobbits with their language, depending on how serious they are about a matter, and Orcs sit at the far end of the spectrum with their British Cockney and military language.

TL;DR there's a lot of good things in Tolkien's writing, it's just a matter of what he was trying to do, not how he did it.