Aurora is Postgres compatible but it’s not equivalent. It was my understanding that the underlying implementation was distinctly different from regular Postgres. So while maybe not as risky as dropping in MySQL, dropping in aurora is still akin to switching to a brand new db and certainly not simple.

Or are you saying they should have started on Aurora from the start?

Yes they should have started with Aurora Postgres. Note that for Aurora Postgres you can just import a Postgres backup and its the same SQL Code. Its Postgres+plus....