This is very frustrating, but I'm not sure it's a problem only with classic JRPGs - recently I sat down to play Bayonetta 3 and it had a similar problem (along with.. others).
FF7 really had this nailed - flashy, mysterious cut-scene to first battle in, what, 3 minutes?
It the same with Spiderman: Miles Morales. There are some cut scenes you cannot skip. Worse they they are cut scenes that don't actually affect the main story arc.
This makes replays painful as the story isn't particular interesting and in some places actually quite nauseating to watch (Miles is constantly conflicted on very straight forward things), but the game play itself is quite fun. I've looked for a mod for this game where you can skip all cut-scenes but it doesn't seem to exist.
Most of the Final Fantasy games have been like that, which is why I've (most of the time) been a fan since since FF4/2. I can't remember how many times I've been turned off by a game when it starts with the protagonist being woken up by his mom, followed by endless wandering around town.
FF7 really had this nailed - flashy, mysterious cut-scene to first battle in, what, 3 minutes?