" Apple explicitly said that binaries are translated at the moment of the installation. "
Not sure what you're arguing with here, but Apple said it did this...among other things.
They said that they have that (when you install the app, it is automatically translated), AND that they also provided patches to various JITs to allow them to output the new native code in place of x86.
Also, it's a translation and not a re-compilation. Finally, Rosetta 2 must be present during execution (in case it also needs to do runtime translation).
Translation and compilation are the same thing, to the point that in German they are the same word "Übersetzung". Translation just by replacing some instructions with other ones and not applying further optimisations is just a very simple for of compilation. A more usual "C" compiler translates human readable source code ito machine code. So, yes, Rosetta 2 is NOT re-compilation from the source, but you can use current binaries as a description for a state machine and then re-compile the latter to a different architecture. This is not a novelty in computer science.
"Also, what the system is now doing is basically using the intel binary as the source code for a new recompilation."
And here is this bullshit again. I wonder what Apple presentation said this to dupe so many ignorant people.
Disclaimer: I am one of the Senior Principal Architects in ARM's Architecture and Technology Group. You know, the team that designs and maintains the Arm architecture. Perhaps you should be careful with your words. Apple said that Rosetta 2 automatically translates applications at install time. Whether this is in fact actually done once you drag an app onto your disk, or lazily the you first open it, or lazily and gradually, with cached translated code, is completely irrelevant, in effect.
"Or there could be continuous optimisation performed under the hood."
LOL, sure, while only doing the "re-compilation" once.
Yes, there could be a simple initial translation, and then analysis of the code sections the take up more time and are executed more often, which could be gradually replaced with more optimised versions. Microsoft does that already. As other technologies previously.
Before engaging in these arguments, please inform yourself.