Why don’t Americans read Shakespeare in contemporary English, or Chaucer in contemporary English? That’s not the way Shakespeare of Chaucer sound.
If you have studied phonology (聲韻學）, you should know that there are endless debates about the pronunciation of Middle Chinese, not to mention local accents and so forth. Wang Wei was born in 山西永濟市 Yungji, Shanxi, but his family came from 祁縣 Qi. Can you with complete confidence replicate his pronunciation? 白居易 Bai Juyi was also from Shanxi, but his family was heavily influenced by the Xianbei, and I recall that somewhere he claimed Xianbei heritage. I have no idea exactly what his pronunciation was like.
Of course Tang poetry was not recited, it was sung, but to the best of my knowledge, we do not know with 100% certainty what the melodies were. Not even ten percent. So even if you can replicate Middle Chinese pronunciation, the poets would be horrified if you recited their poems, rather than sang them to the proper melody. Can you imagine how distressed Paul McCartney would be if he came back in a five hundred years to hear somebody reciting “When I find myself in times of trouble, Mother Mary comes to me speaking words of wisdom, Let it be” in what they imagined was a Scouse accent? Or if they tried to sing it and came up with something sounding like Happy Birthday?
But to insist that Tang poetry be read “the way it sounded” is pedantic. For all but various scholars, Tang poetry is to be enjoyed. I do like to listen to people recite Tang poetry in Hakka, Cantonese, Minnan, or Viet Namese, and I have spent more time than I care to remember studying the phonology of the poems, but to me, that is not as important as enjoying the poems.