Those are fair points, though I’d argue the Kylo in TLJ embodies the message of “let the past die”. He doesn’t shed his persona, but he clearly takes it in his own path and separates himself from Vader, it’s made clear that him becoming “a new Vader” was Snoke’s ambition, and he ends up killing Snoke and renouncing that path. Learning Rey comes from nowhere further makes him realize his “legacy” didn’t define who he was. So by the end of TLJ it’s pretty clear that living up to Vader’s legacy is as far from Kylo’s goal as possible. He “kills” his past, incuding his obsession with Vader.
Yes, but as I stated, in a roundabout way him doing all that is precisely what Vader sought to do (but was never able to). Snoke, whether he realized it or not, was there as a test to see if Kylo could evolve into Vader+, which would be a worthy candidate for Palpatine and the Sith of the past to transfer their essence into.