I don't think it matters too much with bench press - simply because the majority of people need to put some size on their shoulders/pecs/triceps/biceps/lats/upper back - and instead they max out all the time and wonder why they can't flex bone or fat. So part of the prescription for bench press is putting on some muscle to flex - which takes some time. And a lot of food.
5x5/3/1 can work but it becomes a crap shoot with volume - it's only 25 reps but it's also 25 slow, fat reps which can fuck with a lot of people. For me, that's where it gets tricky. Every single time I've coached someone personally and their bench press went up, it is always because of getting bigger - so either I have a magic eye/formula when I coach people and that never happens to anyone else or it is a common theme with most people. Again, part of that is understanding programming and what to look for.
So to answer your question - it might work well for you, it might not. I really don't know when it comes to increasing the bench press because its such a finicky lift and I've always sucked at it. Plus, all the effort we put in with the football team is simply getting the kids bigger in the upper body; I no longer care about getting stronger in the bench press.
I do know that in general, you can't keep beating yourself up on volume on the bench press, week after week, and expect to make massive gains. Even our kids back off, especially the ones that have been in the program for 3 years and are at the point where it can make a difference. (Meaning - some of these kids just need to put in work for 2-3 straight years, no breaks before they can even think about periodization, etc.) If doing more work on the bench press makes the bench press increase, do it! But program it correctly. For example, two leaders followed by one anchor cycle.
Again, the big issue with 5x5/3/1 is people start way too heavy and it catches up too quick. If that isn't working for you, I'd recommend:
Boring But Big
Boring But Strong
5's Pro, 5x5 FSL (seems to work for more people than not)
Do two cycles of the above (remember to follow the rules for the assistance lifts) and finish off with 1-2 cycles of pushing PR sets and either 5x5 FSL or higher volume assistance work. Again, follow the rules for assistance work!
My advice is to keep pushing for size in the upper body, keep training smart and trying some different bench press ideas over the long term. I wish there was an easy answer; I'd be a millionaire. Time, effort and fully committing to a process is the only way to know how successful you can be.