I'd also love if we had a 19000 minute minimum. Nothing drives me crazier than seeing teams tank with the high minute scrubs when they could have drafted enough minutes.
In another league I am in, the rule is:
In order to qualify for an upcoming season's lottery, a team's roster for the prior season must have a minimum of 19,000 minutes (the actual number of minutes in an NBA season is 19,680). No appeal from this requirement will be allowed. If an owner recognizes during a draft that he will fall short of the requirement he may (and is encouraged to) appeal to other owners to trade him an excess player who will meet his minutes requirement. This requirement will be waived for a new owner who takes over a team that failed the requirement for the prior season.