I'd go with that, and the persistence of Latin in however locally hairy a form as the Western language of scholarship over that time. The time and place Hogwarts was founded seems about right for that to explain both the Latin and the hairiness thereof in its tradition.
This suggests that Latin doesn't have any innate magical properties in the Potterverse, any more than it has innately holy or rational properties in our world. However, most new spells are probably modified from pre-existing art. We further know that the results of a mistake in a spell are unpredictable, and often wildly over the top. So once something works, there's probably massive reluctance to rework it, and I expect the whole core of British magic is still a great mass of horrible dog-Latin, with each new layer wrapped around it more frayed and randomly adapted for effect than the last.
A more exotic possibility is that the process of converting will into magic actually requires the translation of one's intent into some barbarous jargon which has a clear meaning (so it can set out symbols), but in which one can't get to think straightforwardly and fluently (so that casting and cognition remain clearly differentiated modes). So Latin wouldn't have worked at all in Rome*, and would work badly for a good Latin scholar now - but Latinate hash would work just fine for a modern Westerner.
* Or possibly, and like English spells in England now, would have failed by working catastrophically well - as in the fireball that casts itself unasked inside your cerebral cortex.
no subject
This suggests that Latin doesn't have any innate magical properties in the Potterverse, any more than it has innately holy or rational properties in our world. However, most new spells are probably modified from pre-existing art. We further know that the results of a mistake in a spell are unpredictable, and often wildly over the top. So once something works, there's probably massive reluctance to rework it, and I expect the whole core of British magic is still a great mass of horrible dog-Latin, with each new layer wrapped around it more frayed and randomly adapted for effect than the last.
A more exotic possibility is that the process of converting will into magic actually requires the translation of one's intent into some barbarous jargon which has a clear meaning (so it can set out symbols), but in which one can't get to think straightforwardly and fluently (so that casting and cognition remain clearly differentiated modes). So Latin wouldn't have worked at all in Rome*, and would work badly for a good Latin scholar now - but Latinate hash would work just fine for a modern Westerner.
* Or possibly, and like English spells in England now, would have failed by working catastrophically well - as in the fireball that casts itself unasked inside your cerebral cortex.