All things being equal, I don't think it matters how late you start. Problem is, things just aren't equal. One of the biggest obstacles to overcome is the mental side of pool. The young ones are full of pipe dreams about how great they are going to be, and just don't have any real idea of just what is involved in it. So, they are free to attain what level they are capable of.
The older guys, while even having the talent to become very good, have the opposite mental attitude. Once they have reached 30-40 years old, they have a pretty good idea of what it takes to make it in this world, and just what they are willing to sacrifice to attain their goals. I think that one would have to have an inordinate amount of natural talent and lack of brains to decide at that age to take up pool for a living. And, to really be competitive today, with so many shortstops out there, you better be a higher level shortstop minimum to make it.
To attain that level, you really have to have the dedication. To have that dedication, you have to have a goal. And, at that age, I just don't know just what goal could inspire one to do what it takes. Fame? Not really there. Money? Not really there either. So, the biggest drawback is incentive. Age - wise, one could do it. Mental wise, I doubt it, but possible with the rare exception.