Can a 21 speed Shimano Tourney groupset get converted into a 7-speed? I currently ride a 3x7 Tourney bike, which I’ve upgraded moderately and it is riding nice. I’d like to know if I can somehow replace my 3-crankset for a simple one, and also get rid off the front shifter and its cable.
Yes - note that some bikes will still need the front derailleur to help prevent the chain from falling off, which defeats the lightness goal, and only makes the bike slightly simpler.

You'd use the upper and lower limit screws to force the FD cage to an appropriate place, and then can remove the cable and shifter.