You're right, OP. Uncharted, on normal or even on hard, is still a fantastic third-person shooter. Most of the encounters do really rely on you, as Drake, to be scrambling from cover to cover, kicking ass and taking names in the process. With grenades, rocket launchers, sniper rifles, etc, it forces you to make use of the game's combat environments to really survive.
The issue is, once you begin to play on Crushing, this all goes to pieces. Enemies become difficult to kill, which wouldn't be bad on its own if it weren't for the fact the game loves to throw a bunch of them at you simultaneously. The scrambling nature of combat is cancelled out by the fact that 2 or 3 shots will kill you, making it more risky to move around in combat. That, combined with the grenade spam and the inability to throw them back in 1 & 2, gets you stuck in situations where you just need to get lucky to progress. In 3 (the only one I've successfully completed on Crushing), the set-piece moments (cruise ship shootouts, jumping from horse to truck to horse again, Ubar and the djinns, the escape from Marlowe's hideout) all become exercises in frustration because of the coalescence of all these factors. The cruise ship shootout sequences alone give me Uncharted PTSD because of how I survived by the skin of my teeth due to luck and gaming the mechanics to survive. That is arguably the games' Achilles Heel. The cinematic experience you get is because of this carefully balanced set of rules governing combat, making it so its doesn't become frustrating and makes you feel badass. When you bump up the difficulty, the rules all fall apart and every combat situation is a moment of dread instead of anticipation.
