What you just described is called "having alternates/back-ups/spares". Almost any type of competitive dance team will and do have them. Just have one team and make your weakest 4 dancers alternates. I'm assuming that the local team does non-competitive performances. But having that team be 16 creates logistical issues. If you have 1 person who cannot do the 16 man routine, then you have no options for the non-competitive performance. Creating one 12 person team allows you to:
1. Only have to create one 12-person routine as oppose to formations for 12,16.
2. Continuous practice of only 1 routine. If people have to memorize 2 sets of formations, 1 for competitions and 1 for local, then you're wasting time.
3. Have 4 back-up dancers that show up to your practices and practice with you which ensures that you will have 16 dancers potentially ready for any 12 person performance whether competitive or local.
An alternative method is to determine 8 core-dancers, your strongest, smartest and most dedicated dancers. The remaining spots are up for grabs. The remaining 8 people compete for the remaining 4 spots. This is better than having back-up dancers, because dancers are forced to maintain their spot if they are not core. Back-up dancers will often quit or not work as hard if they dont think they'll have a chance, so this method would help alleviate that problem and solves most of your problems, for the most part. (Dancers may have to learn new formations depending on the "spot" they take, but its only 1 routine as oppose to a 12 man set and a 16 man set.