Ordinary modern people feel the beauty of ancient poems, not because they feel the rhythm, but because they are ancient poems and feel the "rhythm".
It is difficult and unrealistic to really understand it deeply-for example, the metrical poems in the Tang Dynasty were so developed because the imperial examinations were about metrical poems at that time, just as the CET-4 and CET-6 are so developed now.
The problem of rice and level cannot be just a matter of appreciation.
As for what you said, "Modern people can't really appreciate ancient poetry", it is not impossible, but the appreciation ability has indeed "deteriorated", partly because of the differences in pronunciation between ancient and modern times, as you said.
Part of the reason is that it is unnecessary.
Ancient poetry has become an unimportant culture, dispensable, just like a personal hobby. There is no hard and fast rule in school or country: you can't get a bachelor's degree certificate if you don't pass CET-4, right?
Another problem is that modern people's appreciation ability is deteriorating, which is actually a very normal process. Ancient poems are "ancient" poems after all!
It would be really strange if modern people could appreciate ancient poems as the ancients did, wouldn't it? Haha's laughter ...
So I personally feel that this phenomenon you mentioned does exist, but it is not simply because of different voices or complicated rules in ancient and modern times, but because the times are changing!