TCPs are an economy of force TTP that is as much PSYOP as it is law enforcement. It tells the people who the owner of the street is, and seeing that 90% of TCPs are manned by ISF nowadays, it demonstrates to the population that the ISF is taking over the security/law enforcement role.
If in fact you "own the street", it's not because of the TCP. It's because of a whole range of other actions (none of which are necessarily economy of force) that you are employing concurrently.

TCPs (by doctrine?) are static, and passive actions. We can't win COIN through passive means.

Oh, and if you run a TCP only on easily controlled streets and routes, there's not much PSYOP to it as the bad guys continue to run the ratlines elsewhere because "there's IEDs down in that zone" statements speak volumes about risk aversion. The locals know what's up.