It is an interesting theory, for sure. Instead of countless 3-dimensional particles, you have a single (or very few) 4-dimensional objects. You can imagine it like a sheet of fabric that is our present, with everything above the sheet being the future, everything below the past. When you want to sew a thread (our electron) through the sheet, you need to pierce the fabric, but to do it again, you first need to piece it the other way, giving you a positron. You can create or destroy arbitrary many of these, but you need create or destroy one of each every time. More interestingly, it is exactly determined which two will annihilate each other, as the allegorical loop of thread gets pulled tighter and tighter until it gets pulled though the sheet. The universe would be deterministic.
I'm sure there's a myriad of contradictions to modern QM and particle physics, but it's fun to think about nonetheless