that would be nice but if it was led by NASA (aka contractors like jpl, lockmart and boeing) there's no way the sats could've been produced as cheaply and quickly imo, because NASA's strengths lie in experimental/science focused things, not operational things

also they wouldn't get the in house pricing for Falcon 9 launches that spacex gets, and spacex wouldn't be able to use starlink launches to test out new boosters for crew launches

i mean there's nothing stopping NASA from doing it (aka Congress funding it and telling NASA to do it), it's not like spacex is going to turn down customers for their rockets