It can work out well, and it can be a disaster!
My racing bred QH gelding, who will be 17 this year, was purchased fall of his 2 year old year. He matured really nicely, and would have been amazing, but he was one of those never quite sound horses. He seemed fine the first few months under saddle as a 3 yo though, so this could have happened if I’d bought him a little later as a started prospect. I found out later that he had been borderline starved, and I suspect that nutrition was lacking for proper development of his 17H frame. He eventually shattered his mediocarpal bone in a way that suggested that his bones are less than strong.
My first warmblood, I also bought fall of her 2 yo year, from a small breeder with a good reputation. Did my research and bought ammy-friendly bloodlines. Mare had some odd sensitivities that I didn’t translate into potential problems under saddle. Got thrown, put her with a western trainer who got her in a wreck, spent 18 months with another trainer who was the best option for repairing a wrecked horse, then eventually got rid of her. Found out later that her dam never performed under saddle because she had bucked off a bunch of pro riders.
Currently I have another WB mare that I got as a 2 yo. She is a little late in her training because she had OCD surgery spring of her 3 yo year and it took 3-4 months before she came sound. However, she has turned out nicer than what I think the breeder expected her to be, and seems to be sane and sound, if not rather obstinate and clearly not one who has read the books on how young horse training is supposed to progress. So hopefully third time is the charm!
In five years or so I think I might go down this path again to hopefully get a GP prospect, but will probably have the horse professionally started. I felt the need to back my current horse myself to get past the baggage of mare #2, but doubt I’ll want to do it again when I’m five years older.
I’m also trending towards not starting horses until they are a full 4, and find that having the year of doing ground work and really getting to know the horse is valuable. I probably would have started current mare summer of her 3 yo year if not for the post-surgery lameness, but now I’m glad that I spent more time. To that end, the one critique of your plan that I have is that I would want to have the horse with me for at least several months before the serious training starts, to build that relationship, rather than having it in a field at the breeder’s.