When they stop growing in height can sometimes depend on blood line.
I can't speak to the newer "models" but my coming 20 Generator fella had a growth spurt at age seven that took him to 16.1H. He was always gangly looking and hip high no matter how much I fed him. The last two years I've been trying to take weight OFF because his long athletic-built self does not look good with extra pounds.
The fella in my avatar is more "Morgany" looking (a Morgan mare is the TWH foundation mare of record). Even though his sire, Pride's Genious was well over 16H, my fella topped out at 14.3H and filled out by the time he was four or five; I can't remember as he is now 26 and we've been buds 23 of those years.
Also, that stocky little 14.3H guy in my avatar has such a natural awesome reach that folks comment on it when he is 1,000+ feet away, at liberty in the pasture. It's been commented to me there are TWH's "with twice the leg" that can't get under themselves like he can". As someone else said, the horse either has the reach or it doesn't
My third TWH, who will be 19 this year, was coming 12 when I bought him; he had his height and had already "blossomed"
As an FYI, he is built like the horse in my avatar but is 15.3H and comes from very old timey Plantation stock; both his parents were in their 20's when he was foaled.
If sounds as if your vet has given you great advice. If your fella is on the gangly side believe me that will be a huge athletic plus once he gets his legs under him (don't push that as TWH's are generally 3 or a little older before they finally find their legs and their gait.
My two stocky built TWH's deal with insulin issues, to-date the lanky athletic guy (who was gangly as a young-un) does not.