The problem in skipping the legal process is twofold. First, if you establish the principle that a citizen can "lose" their right to the presumption of innocence and a fair trial then they're no longer rights, are they?
Second. if you even once give some government official the power to take away someone's legal rights -- because we all agree the defendant is guilty anyway -- then you've made it possible for a future government official to take away someone's legal rights in a case where maybe everybody doesn't agree the defendant is guilty.
This is how people lose their rights. It always starts with stripping away the rights of the least popular.
Anyway, I have trouble believing someone is seriously arguing this. The bottom line is, there is zero chance that this is going to happen. So in that sense this argument is entirely abstract.