"is it completely irresponsible to split the hive 50/50 and not care where the queen ends up, one box or the other? And, let the queenless hive generate their own queen? I am seeing only one major drawback, losing nearly a month for the process."
blue, like g said, this is a walk away split, and i am not a fan of them, the odds are against you that the colony will fail. a queen raised from a walkaway, if successful, you will be looking at about a 7 week delay, so anywhere between 49 and up to 60 days when the colony raises it's own queen. on the positive, varroa control because of the brood break, but costly in terms of colony buildup. to the raise a queen from viable larvae, emergence, maturation, mating (if successful) and egg laying, then 21 days for worker brood to emerge, and in the meantime your population will drop from this colony because no new bees are being born during this period of time. this can and does affect what resources come in the front door and comb building, and don't expect a honey crop the first year.
i think it is a great educational experiment to try at some point, too many variables that contribute to failure. i have done them in the past. my rate of success at this seems to lean more towards the failure side. not saying it doesn't work sometimes, but if it fails, then a beek is facing a different set of problems to remedy in the process; for example, if not 'managed properly', a diminished population of older bees, and possibly a requeening challenge.