I am not an expert on D3 JV programs. My son's school had a JV program for a year or two; I don't think it is still in existence.
You can learn a lot about a program by looking at the past 3-4 years of stats. What you will see is in Year 1, you will have 9-13 position players that play the majority of the innings. Then you will have 6-12 position players that will get a few innings and a few a bats (difficult to define a few until you look at the stats). Then in Year 2 as the seniors from Year 1 move on some of the 6-12 players that got playing time will move up. In addition, you will add a new class of freshman. Some of the Freshmen will be part of Year 2's players that play the majority of the innings and some will join the 6-12 that will get a few innings. Year 3 & 4, the process continues. The good players move up, the good players that are recruited will join in and the cycle will continue.
Then the question is where do JV programs fit in. I am not an expert; but it takes a commitment from the University, it's coaching staff and the athletic department (to fund a JV program). I would expect most D3 programs to follow the model that I have outlined. Funding a JV program is a terrific way to keep players that may not play engaged with the program. In that there are not that many (from what I have seen) I question if they can make a big difference in the competitive profile of a given program.