That's why you simply don't flush them. I've got a separate bin where I toss my wipes. The ones I buy are only ever made of plant fibers and contain no plastics and so on.
Yes, they can cause a lot of problems, and they shouldn't be marketed as "flushable". If you don't flush them, and if they're not cheap plastic, they're not necessarily bad. In terms of wiping your ass, they're superior.
Wet toilet paper may indeed be equally effective, but in my experience it's inconvenient and more difficult than either using wipes or toilet paper. Wet toilet paper collapses easily. Most wipes are designed to have enough integrity that, to put it bluntly, you don't need to worry about getting feces on your hands or drip poop water everywhere.
If you find wet toilet paper effective, that's great, have at it, but I think it stinks (figuratively and in this case literally).
