I agree with the others who have stated that changing the regulations is not going to fix the problem. The people who leave them out are not the ones who tag their lines and check them regularly. A large number of trot liners go 2 or 3 times a year and pull their lines when done.
As far as the enforcement thing goes, some things are just not practical to enforce. To legitimately enforce even the regulations we have now is beyond TPWD, they simply don't have the amount of wardens needed to pull it off. Can you imagine the amount of hours needed to go out looking for illegally placed trot lines, or worse still the amount of time it would take them to go out and clean them up? I don't think they should officially authorize anglers to go remove them either, who is to keep other anglers and such from cutting the legit lines and "losing" the tags?
Folks, about best thing you can do is leave the legally marked lines alone and cut the trashy unmarked lines. Keep your mouth shut about doing it, and throw them in a dumpster on the way out of the lake. If anyone asks say something to the effect of "It hung up in my prop and I didn't want to just drop it to the bottom". Yeah that is illegal, but if you want something done that is your best bet at getting something done and it would be really hard to charge you for untangling a line from your prop and not dropping it back in the lake.
Personally, I don't mess with any of them. I don't like running into them or hanging up on them, but they do not belong to me and that is that. I wish people would clean up after themselves, but these days many people do not, government regulations will not fix that.