I wouldn't say it ever gates your progress, but I do think it does a very poor job of creating a smooth feeling of progression, which is exacerbated depending on which order you do the divine beasts in. For example, if you do Naboris relatively early on, the game will demand a relatively high level of skill and combat mastery to get past Thunderblight which just isn't present for any of the other bosses. In other words, the game makes you get pretty good at combat, and then every other boss for the rest of the game is an utter pushover because you've improved so much and they don't require anywhere close to that same level of skill.
On top of that, the abilities you gain from defeating the Blight Ganons, along with the huge amount of healing items you can take with you, make it far too difficult to die mid game onward imo. There's a degree of challenge present in the early game that just disappeared for me from Naboris onward. Being able to heal from essentially anything, along with three free shields on any attack and a respawn + extra hearts for your first death make it way too difficult to die.
Perhaps the difficulty curve smooths out a bit if Naboris is your last divine beast, but that just feeds back into the issue of the openness of the game allowing for the curve to be distorted.
Oh Thunderblight is a spike, I agree on that, he should definitely have been brought more in line with the others. But otherwise I thought it scaled fine; the player does get much more powerful once you have the Divine Beast abilities, but I thought this boost in strength was helpful in taking on tougher challenges later, like fighting Lynels and ultimate Hyrule Castle and Ganon.
That's actually my problem; my complaint isn't that the curve distortion makes part of the game too hard, it's that it makes the rest of the game too easy. The boost in strength that you mention is too helpful. The gap in skill demanded between Thunderblight and the other bosses, combined with the near infinite amount of healing items you can take with you into battle and the overpoweredness of the champions' gifts, meant that I was almost never in any real danger of dying from Naboris onward, including the final boss.
To try and put things concisely, the start of the game + Naboris demands that you pick up a bevy of survival and combat skills in order to survive. The limited amount of healing items you have at the beginning of the game and the low quality of your equipment, combined with the difficulty of earlier encounters such as the first Lynel and Thunderblight, means that BotW requires a high degree of skill from the player in the first half of the game. In other words, you have to "git gud." And that's a good thing; I tend to prefer games that challenge me.
My personal complaint is that the second half of the game doesn't keep up the same degree of challenge. After Naboris, you acquire three powers (Mipha's Grace, Urbosa's Fury, and Daruk's Protection) that make combat much easier. Simply by virtue of having played the game for a long time, you've almost assuredly found much better gear and weapons, and accumulated a large number of healing items. And, on top of all that, you have the skill you've developed from the first half of the game. You've gotten better at combat from having to fight Lynels and Thunderblight, and you've learned the ins and outs of surviving in BotW from the earlier parts of the game when you didn't have good equipment or healing items to fall back on. This should have been when even tougher enemies showed up; to force the player to master both the skills they've learned so far and the better armor and weapons they've found. The challenge level should have ramped up to match the increase in the players' skillset and improvement in equipment. But it doesn't: the enemies don't get any tougher. In fact, I think you can make the argument that they get easier. Personally, I think that Windblight, Fireblight, and Calamity are all easier than Thunderblight. I rarely felt like I was being challenged past Naboris; the game forces you to develop all of these combat and survival skills in the first half, but then never requires you to use them past the halfway point.
This may all just be a matter of perspective and what kind of difficulty you're looking for in a game, but I thought BotW could've been improved significantly by making the latter half of the game demanding of the player in the same way the first half was.