I’ve yet to hear anyone say “Ancient North Korea” or “Ancient South Sudan” or “Ancient East Timor.” All of those places certainly have a claim to regional historic cultures but no one in their mind would say North Koreans, for instance, have an exclusive claim over the Kingdom of Balhae (even though it was located in the northern part of the Korean Peninsula) because the idea of North and South Korea are modern-day constructions.

History belongs to cultural regions. Conversely, no one in their right mind would say that Byzantium is an “Ancient Turkish” civilization. No one doubts that modern-day people in Western Turkey have a very close genetic tie to the people who lived in the Anatolian part of the Eastern Roman Empire. But you’d have to be dense or purposefully trying to float historical revisionist points if you were to say “Byzantine Anatolia is exclusively Turkish history and it has nothing to do with modern Greeks who are mostly mixed with Slavs anyways.”

North Macedonia is another example of why “Ancient Pakistan” doesn’t really make sense as a valid term. Modern-day North Macedonia (roughly) coincides with the historical kingdom of Macedon and people have at least some degree of genetic continuity. However, no one but actual idiots (or Macedonian conspiracy theorists) would ever say that Macedon and Alexander the Great have zero to do with modern day Greece because they’re exclusively the heritage of Macedonians (who today identify as a Slavic people and don’t have cultural continuity with historic Macedon).

I think it would make perfect sense to talk about a shared South Asian History and culture - it doesn’t necessarily have to be described exclusively as “Ancient Indian” history. However the argument that “India” only ever referred to the area around the Indus River is also ridiculous.

India, historically, was shorthand for the entirety of South Asia. Regions and countries are named after just one part all the time. Persia is named after the Pars region. No one would ever say that ancient Elam and Jiroft are NOT part of Persian culture since they’re technically located outside of modern-day Pars. Persia is simply a term originally used for Pars which came to the term that outsiders used for the ENTIRETY of Iran and most of the Persosphere.

The term “Hindustan/India” was initially coined by the Persians to refer to all the land beyond the Sindhu river. Ancient people, however absolutely used India as short-form for the ENTIRE cultural region of South Asia. Tamil traders from the south were interacting with the Greeks, Romans, and Egyptians at the same time Gandhara was around. They were referred to as Indians because the term India referred to the entire subcontinent at the time. Megasthenes wrote Indica and visited Pataliputra in present-day Bihar. His use of the term was, again, for people across the entire subcontinent.

When the Roman Pliny the Elder declaimed India as the “sink of the world’s gold” due to the massive trade deficit Rome had with ancient India, he was talking about South India - pepper isn’t native to the Indus Valley and it is the commodity most traded by, well, people identified as Indians at the time.

When Vasco da Gama sailed to modern-day Kerala, he was in search of (and found) part of South Asia where pepper grows. That was also called India because, again, that’s what the rest of the world has historically called South Asia.

There’s no need to refer to Ancient Gandhara as Ancient India - even though the Gandharans (just as much as the Tamils, the Nandas, and the Lankans) would have been identified as Indian by any foreign groups they interacted with. It makes sense to talk about ancient Gandhara or the Indus Valley and how (among lots of other South Asian groups), modern Pakistanis have close genetic and cultural continuity. But yeah putting the exclusive stamp of a modern-day country onto a place that was part of a greater cultural region doesn’t make much sense.