A fighter using Booming Blade means not benefiting from its Extra Attacks. It’s nice at low level, but replacing 1 or 2 of your swings with some damage if you hit is situational. See this analysis. There are utility cantrips. For use in combat I’d pick a ranged damage spell and Mind Sliver is only Verbal so no need to free a hand up.
Try it! Your ideas are sound and playing for a gimmick can be fun!
I’m about to start using a Fighter whose whole thing is shield bashing to shove enemies around and I expect it to be bad in most encounters.
I played a Ranger with Booming Blade and most of the time I didn’t use it, but when I did it was very satisfying.