WTP – interesting idea, but it might make it hard to keep certain Mitzvos like eating 3 seudos on Shabbos, bentching, making brachos, davening, greeting people, being friendly and nice to others, etc…
Also if you attached the tape in such a manner as to close your lips, I would think you’d be in more danger of inadvertantly ripping off lipskin with the tape anytime you breathe or move your lips at all.