My son was a failure as a hitter. He didn't hit in t-ball, Pinto - at any level. But he did his swings every morning for 15 minutes and every evening for 15 minutes from the time he got serious hitting lessons from the local NAIA asst coach (now HC Arizona) from age 11.
That coach was who set up his regime. (And, yes, swings which are not done properly are worse than nonproductive; and a kid who is forced to do it won't do it correctly.)
I looked at swing time (as we called it) fondly - I got to soft toss and watch (often loading the tee) and we got to talk. He knew he wasn't a good hitter, but he did all he could to improve - and he knew he left nothing to chance or luck. When he stopped hitting lessons (end of 11th) it was with the knowledge that he just didn't have what it took to be a great hitter. (He did hit well over .400 in HS; in a bad, bad league.)
There is no correct number of swings (or any other drill); the variables are many - the player's desire (not stated, but actual work), conditioning, goals, other commitments, etc. But I can say this for anyone trying to make it to college ball: someone, somewhere, there is a player your age working harder, taking more reps, and trying to take that slot in college.
For parents going through this for the first time, ignore what the other kids are doing, ignore the urban myths, legends and lies. You can only control what you can control and that includes the quantity and quality of work you put in - recognizing that there are no short cuts, the improvements are incremental and not even linear (e.g., growth spurt upsets the apple cart).
But, NOTHING substitutes for hard work over long periods of time - and if you are doing this for the first time and have long term playing aspirations, you can't even imagine how fast the game gets, how much work it takes just to stay even with your hard working peers, much less gain on them.
A player can't control his coaches, his fielders missing pop ups, or the weather; but the player has absolute control over how hard he works - and whether he can answer the question when he finally hangs up his cleats: Did I do all I could to reach my goal (whatever that goal was: HS, college, whatever)? An answer of "no" represents failure.