2012 egr cooler leaking

Just purchase a 2012 started seeing white smoke and that sickening sweet smell of antifreeze burning, before looking to replace head gasket I unplugged the EGR vale and no more smoke, upon further research, and discussions w/ other mechanics the thought was even after replacing the cooler by driving car w/ EGR unplugged The car gets better mileage better performance, with check engine light on. the thought process is since you are not reburning spent exhaust you have a cleaner running engine with no worries about the port clogging especially on 1st cylinder causing notorious head gasket issues. Curious on other thoughts out there? When Cars due for inspection wipe code plug in EGR valve to inspect.
Also I was considering even bypassing the EGR cooler antifreeze lines What would be the effect, bypassing the cooler while keeping the EGR unplugged?