Out of curiosity I tried your method for 3 rolls. Overall not a bad distribution.
11,12,14,14,10,14 (No points left over)
15,13,9,13,12,11 (3 points left over, 1 STR, 1 DEX, 1 CON)
11,13,15,12,13,10 (2 Points left over, 1 DEX, 1 WIS)
I suppose a rule like "If you have 1 excess point from a higher stat you may move that point to a lower stat, if you have 2 or more excess points you may move a point from one stat to another that also had an excess point. Odd numbers of points may be moved to a lower stat according to the prior rule." (Im sure that could be worded better.)
Hypothetically this is a self-balancing system. Even if you get none of 2 numbers the others should result in stats of 14 or 15.
Probably decide on a stat cap or point value for stats beyond 15, (11 or 12 points for a 16 etc.)
Overall interesting enough for me to keep in my back pocket if one of my groups ask about rolling stats.