Big Mom has done one thing few other villains could: she changed Luffy's behaviour.
Character development, both positive and negative, tends to be understated and slow-burning in One Piece, but it's certainly not nonexistent. Let's talk about Luffy's character arcs in the New World. The first one, I think, starts on Fishman Island when he promises to "protect everything." This isn't something Luffy needs to grow from, necessarily, but it's an assertion that needs to be challenged and then tempered to be more realistic. This happens on Dressrosa, and I wish it had been brought more to the forefront that it was happening. As it's been written it's more of a vague, slow, background development, and a personal through-line for the protagonist could really have unified Dressrosa's generally chaotic lack of focus. Essentially, Doflamingo, manipulator, physical and mental puppetmaster, has the perfect toolset to make protecting everyone and everything impossible. There's no keeping the Birdcage from destroying Dressrosa (though thanks to the teamwork of Luffy's allies its people are saved), Law was nearly outright murdered with no way for Luffy to intervene, and Bellamy, well Luffy had to put Bellamy down himself, even though they'd become friends just hours before. Protecting everything was really thrown out the window there, and I wish we'd been shown more of the turmoil Luffy felt over that instead of just the broad "you hurt my friends, Mingo!!" rage we got. Regardless, Luffy grows from this experience and demonstrates a more realistic kind of resolve through the Tottoland Saga, accepting the sacrifices of Pedro, Pekoms and Jinbe instead of throwing everything away to not leave a man behind. He's far more willing to go for the better net result instead of making it all or nothing, which is a sharp contrast to his attitude at the start of the New World.
The second arc, as established, begins with the Fujitora fight, and is, as with the last one, challenged in the very next major saga. Luffy comes up against a foe he can't defeat now, in the most literal way possible, and is forced to retreat. I don't think he's truly compromised on his decision not to back down from foes perceived to be above his level just yet, as he flung himself right at Kaido and is training to do the same thing again. I think he sees Big Mom as a lone exception to his declaration. We can see from the way Luffy reacts to her storming into the prison he's strongly associated her with the desperation and losses of Tottoland and still sees her as something totally unbeatable, that can only be run away from, even though he's just been training to face her apparent equal, Kaido.
Very good analysis, I agree with everything you said!