I block first and 6th strings when I play sexond shape
That seems like a good idea.
Not unusual to find a C chord with a G bass. For that matter many chords can be written with a note other than the root in the bass. A lot of country and folk player use this technique. It can sound good especially when playing alone. But, it can get muddy if playing with others or in a group that has a bass player. Don’t want rhythm competing with bass.
As you rightly pointed out, in a band setting or when playing with others, it’s essential to be mindful of the overall balance. Having multiple instruments playing in the bass register can lead to a muddied sound, affecting the clarity of the musical arrangement.