Another thing to consider is your FH to BH transition. A neutral grip helps, but there are other factors. Being in great position is number one. Keeping the bat belly button to chest high is important. Starting the BH stroke, whether it is a low spin drive or a spinny BH loop, against a topspin ball in a rally, you start the stroke from the same high point. Another thing is to NOT impact the ball too far in front of you, that causes you to NOT use your entire body for a stable base. That makes you use your shoulder only for support and that is not enough. Whenever we lean and try to make a shot other than a block or low power shot, there is no control at all. Another thing that hurts a lot of players BH shots who favor a FH grip is the anticipation and position after the shot. FH happy players often do this... instead of keeping the bat in middle ground ready to go either way, the Fh happy player already instinctively brings his arm back to be more ready to initiate a FH shot. Then, when the ball comes to the BH wing, they have to reverse their thoughts, wake up, get arm back to middle, and try to make a BH shot. Result is usually a fail.
I say all that to illustrate that the grip isn't the only thing that wrecks a player's BH shot making. Usually, it is something else. using a FH favored grip, a player can still land BH shots, it is just that the those BH shots will normally carry less power, spin, & speed than a neutral or BH oriented grip.
The BH, at lower levels is a much more effective shot that either directly wins points or greatly contributes to winning them on the next shot. Why? The BH involves very little backswing (vs an incoming topspin ball like in a rally). Thus, it can be VERY difficult to see the direction the ball will go. Plus, you can easily disguise this, PLUS you can get the BH shot into action very rapidly with a high degree of safety if position and other aspects are correct, PLUS you greatly reduce your opponent's reaction time, PLUS you can exploit his weak zones, PLUS you can easily change the spin and it is harder to see as the action happens so fast.
Who at the lower levels can step around everything 100% of time and make winner after winner after winner or get to the block down the line or cross court after making a FH? No one (at that level) is the answer. usually, the lower level players are already off balance on their FIRST FH that makes them move, so cannot get to the block if they hired James Bond himself to drive them to the course of the block.
That is why I emphasize the importance of a good BH. In addition to all these other things, it allows you to make a quality winning or pressure shot while keeping some semblance of position for the next ball. It also allows you to have another thing for the enemy to think about. if the opponent gives you a ball to your body and you make a strong BH topspin suddenly anywhere unpredictable, it can really trouble them. if the opponent avoids that area and gives it to your more dynamic FH zone, you hit a strong topspin down the line for a winner and now the opponent knows you just ripped his head off like one of those video games and finished him.
at the higher levels, it isn't this easy or simple, but the same principles apply and opponents are much better at using your lack of BH pressure as a thorn in your side.