The reason that I reminded you of her is that, as howtheduck has noticed, Brian appears to serve the same function for Mike. He sort of hit the ground running by doing something Mike never does: tell his mother about what's going on at school. He also applies himself in school because he can't allow himself to turn in bad work, refuses to back down from challenges, points out glaring flaws in Mike's logic, tells Mike to his face that he's a lazy slacker and witless goofola who makes excuses for his being a lazy slacker and tries to pass the buck when confronted with the blowback from being a witless goofola and (most importantly) informs his mother to tell Mike's mother when he's done something that will heap disgrace on the Patterson name and risk the disapproval of the free-lance shame brigade that the mother from Little Iodine lived in fear of.
In short, he's the Ideal Child who Michael should aspire to be; such is his perfection that he exists to remind Mike of his duty to study and work and strive and not complain about doing his duty to make up for having to mildly inconvenience his idiot boomer parents by being a vending machine built to compensate for their made-up life of privation. Since Mike was born in an environment where he grew up dealing with Elly's madness, he has never figured out that his friend is his mother's drone meant to keep him in line. Since John had a life before Elly, he sort of vaguely resents having his wife's loudspeaker in his office.