This is a naive question... But I realized that auto-regressive predictions can be inherently unstable due to previous prediction error monotonically accumulating in the inputs: $M(h_{t-n},...,h_{t-m},p_{t-m+1},...,p_{t})=p_{t+1}$ (e.g. LSTM/GRU type models). And I can only think of one application where auto-regressive predictions' "self-consistency" would be worth it: text generation (...otherwise text would be gibberish).
But for regular time series: Why not directly predict/query time-step(s) independently, given only historical observations? That is, independent of any potential intermediate predictions: $M(h_{t-n},...,h_{t},q)=p_{q}$.
Context: This auto-regressive instability is a big problem (for statistical models/surrogates) in the computational physics community and it seems they prefer to avoid the problem altogether in exactly the way I described.
