I hate the Timless Child as a concept, but it doesn't really ruin anything because the Doctor has no recollection of those lives, they have no bearing on the personality of Hartnell through to Tennant 2.0 (or is it Tennant 3.0?) that's actually part of what I dislike about the concept. the Doctor can't be lauded or castigated for anything they did in a pre Hartnell incarnation because they don't remember it, they were effectively a different person.
I prefer to consider the Doctor as just A.N. Other Timelord, one who ran away from Gallifrey because they didn't fit in, rather than because they were super special, but the good thing about the Timless Child is that still works. As far as the First Doctor was concerned, they were the First Doctor, and that is why they left. That perhaps this desire to run away was prompted by some hidden crumb of knowledge buried deep in their subconscious about their true origin is neither here nor there, YMMV and you can choose either option.
TTC is the worst kind of epic change to the concept of the Doctor, precisely because it doesn't really change much. Not in the way that the introduction of the Timelords or even the War Doctor did.