In reality, you put your fingers in the position for a C on that specific instrument and you get a C. The name "transposing instrument" is misleading; the instrument itself does not transpose. It's purely a notation convention, intended to give you a consistent mapping between notation and fingering so it's easier to switch between instruments. If you only play one instrument there's no need for it. And even if you do, it's not strictly necessary, e.g. recorders are commonly available in both C and F and are conventionally not notated transposed. Professional players routinely switch between them for different pieces.
I expect it would be possible to train an image-processing LLM to OCR sheet music so it can be automatically transposed and re-engraved for compatibility with absolute pitch.
OK, my fault for poor communication. Let me try strongly typing this.
Clarinet: you play a finger-C, out comes a soundwave-Bb. Flute: you play a finger-C, out comes a soundwave-C. And finger-C is polymorphic on the instrument, or something.
Aside from that, I don't disagree with you.
One consideration is that with most instruments, being keyed the way they are, if you immediately transpose via LLM some of those instruments will have almost all their notes in unexpected ledger lines.
Which could have (en)grave implications.