I.... like the idea. I'm glad they give us a reason why the character can regenerate more than other Time Lords, and it makes sense. I hate that they practically killed off the evil mastermind who tortured The Doctor like it was nothing. That character should have been a series-long villain.
The issue is that it was already established why the Doctor could regenerate again after Matt Smith.
The Time Lords gave him a new cycle in Matt Smith's final episode, which he commented on.
Additionally, it was established in 1976 that Time Lords could get a new regeneration cycle if they basically pulled off some chicanery (The Deadly Assassin). The Master was at the end of his regeneration cycle and somehow managed to garner a new one (see Keeper of Trakken/Logopolis/Castrovalva).
The biggest slap in the face is that it breaks established lore and considerably ruins everything about the character as we had come to know him. The Doctor, in the beginning, albeit mysterious, wasn't anyone special. By Time Lord standards, he was more or less a renegade idiot who just stole his time box. The entire point of the Doctor as a character was that he wasn't special, but because he did good things, had a good heart, and cared about people, he was someone that could be looked up to. Even the viewer, who by many metrics wouldn't be someone special, could make a difference to others by doing good for the world. Not to mention it breaks the (already pretty wonky) continuity of the Chameleon circuit being broken, as established at the very beginning of the show in 1963, by giving the Timeless Child doctor a TARDIS that is stuck as a 1963-era Police Box too.
There were at least five things from the original show that was inflexible canon to the Doctor's identity that have now been stupidly thrown out the window for a shallow reveal that, while it doesn't change the Doctor's motivations, it completely rewrites everything that had been a hardline up to that point:
- The Doctor is an exiled traveler that can travel through time and space (An Unearthly Child, The First Doctor, 1963)
- The Doctor's time machine was broken, and its chameleon circuit was broken to a 1963-era police box. The Doctor could not fix this because it had *just* been broken. (An Unearthly Child, The First Doctor, 1963)
- The Doctor originally used murder, lying, scheming, and cold-hearted threats to achieve what he wanted. (An Unearthly Child, The First Doctor, 1963 | The Daleks, The First Doctor, 1964 | The Edge of Destruction, The First Doctor, 1964)
- The Doctor learns compassion, empathy, and humility after nearly having two of his companions killed in a near-death experience. (The Edge of Destruction, The First Doctor, 1964)
- The Doctor can regenerate into a new body and form at the end of his life cycle (The Tenth Planet, The First/Second Doctor, 1966)
- The Doctor comes from a race of people known as the Time Lords, who control time and space. He has also been on the run from them for a long time. (The War Games, The Second Doctor, 1969)
- The Time Lords tolerate the existence of the Doctor and occasionally assign him on missions they know only he can accomplish (The Three Doctors, The First/Second/Third Doctor, 1972)
- The planet from which the Time Lords live is known as Gallifrey (The Time Warrior, The Third Doctor, 1973)
- The Time Lords maintain a 12-Regeneration cycle, allowing for 13 incarnations in total. (The Deadly Assassin, The Fourth Doctor, 1976)
- The Doctor has been offered the position of Lord High President on no more than three occasions. (The Deadly Assassin, The Fourth Doctor, 1976 | The Five Doctors, The Fifth Doctor, 1983 | The Ultimate Foe, The 6th Doctor, 1986)
- The Doctor wasn't just some renegade Time Lord, but he was also generally considered a below-average, if not less intelligent Time Lord compared to others. (The Ribos Operation, The Fourth Doctor, 1978)
Now then, with those hard-line lore dumps for the Doctor's backstory, there have been more controversial things that have been more or less waved off not just by canon, but by the fandom itself. These have either been completely ignored or not entirely confirmed by future canon.
- The Doctor had more than just his four incarnations beforehand. (The Brain of Morbius, The Fourth Doctor, 1976)
- The Doctor is more than he seems, possibly one of the original founders of space and time travel for the Time Lords, (Remembrance of the Daleks, The Seventh Doctor, 1988 | Battlefield, The Seventh Doctor, 1989 | The Curse of Fenric, The Seventh Doctor, 1989)
- The Doctor is half-human on his mother's side. (The Television Movie, The Ninth Doctor, 1996)
While the Brain of Morbius is perhaps the baseline for the whole Timeless Child idea, it wasn't ever confirmed entirely, and it still never made it so the Doctor was an immortal demigod. The Doctor was still, just a regular Time Lord renegade. The 7th Doctor's secret arc, known by fans as the "Cartmel Masterplan", never came to fruition because the show's canceled in 1989, but it at the very least would have done a lot to actually explain why the Doctor was a renegade and an outcast to his own people. After all, Rassilon was dead, and Omega had been trapped in a negative universe that The Doctor created. It was a bad idea but was still within the realms of plausibility for why The Doctor was the way he was throughout the series. As for the Half-Human Time Lord idea, it was stupid from the start and the fandom and the canon of the show have entirely ignored it.
It was only starting with RTD (and kicked into overdrive by Moffatt) that the Doctor became more than just a strange alien that innately knew what good was. He, rather myopically, became "The Chosen One" when the Doctor in incarnations past would have fucking hated that title and responsibility, and would have run from it at every chance. There's a reason the 4th, 5th, and 6th Doctors all turned down the chance to become Lord President of Gallifrey; they fucking hated responsibility and didn't want to be important. The only reason the 10th and 11th eventually accepted the responsibility of being "the chosen one" was that they were given no other choice but to do that; after all, who else would have saved the universe from something he himself started (and yes, I am saying the Doctor himself is the cause for every universal near-catastrophe). It was the Doctor that caused the Time War. It was the Doctor that ended it with Gallifrey's destruction (and subsequent "rescue"), and it was the Doctor that had caused everything after this.
TL/DR:
It ruined the context of Who (pun intended) the Doctor was. Instead of a rebellious time lord who did good things and became a legend because of it, they're now preternaturally the Chosen One who was born special, was always special, and will always *be* special. If the message of the original series was that "Anyone can be special by their actions.", then by the context of the reveal is that, "The Doctor was always special, and everything they did was because they were special. Nobody else could do what the Doctor has done, because he's so special!"