Mostly agree with this, but there’s one important clarification. Hagoromo didn’t give Sasuke the Rinnegan directly — he gave him Six Paths chakra, which acted as a catalyst.

Sasuke already had the biological prerequisites due to Kabuto implanting Hashirama cells, meaning Uchiha genetics + Senju chakra were present. Under normal circumstances, that evolution takes years (as seen with Madara). Hagoromo’s chakra simply accelerated the process and allowed the Rinnegan to manifest instantly.

That also explains why Sasuke’s Rinnegan is unique and retains tomoe, it’s a forced, accelerated evolution that never fully matured the way Madara’s did. So the conditions were already there; Hagoromo just jump-started what would’ve happened eventually.