... I don't like deep bracket boxes, I feel like they're flimsy.
I have never seen an unbracketed square box mounted to the side of a stud- at least by a professional. I can't see what you are after by thinking the bracket is flimsy. With wood studs no way are they going to move and with metal studs, well, nothing is going to make any difference anyway except far side and back supports.
One reason to use bracket boxes with wood studs that are sometimes twisted is that you can bend the box in or out to keep it parallel to the surface of the sheetrock. Mount a plain box as you do and you would bend the box all up trying to do this, or you could use shims.