How do you know "i don't recognize it"? you just assume. Trust me I've struggled with synchronization of external gear with the PC(never used a mac) based DAWs I've used, not just Live.And then here's yet another person who doesn't recognize it, because it hasn't happened to them. So it must not be real. That never gets old.
Of course direct monitored is never in sync with any DAW, PDC or no PDC, because the DAW doesn't know how your midistream behaves or the gear to it, it can't.
So one solution, the one you think works best for you it seems, is to manually tell it to the DAW for each midistem. Very cumbersome and at worst the delay is not constant and fluctuates. I guess we can agree so far, no?
So the solution for me is to use an external instrument that aligns the audio, instantly without any involvement from me.
Now you might find that laughable with your massive professional studio setup galore.
Answer my one thing though: Does the External Instrument align the incoming audio to the proper midi event, yes or no?