Quote from commiebat:
There's really no advantage to tying up additional cash in the amount of the difference between the strikes.
Tying up cash? He is writing, so he is receiving cash and can receive interest on it. Did I miss something? I see the main problems as rather paying larger bid-ask spreads, he can be assigned on the put side if the option is deep ITM, and also the treatment of margin can be different.
Strangle with ITM call and ITM put is a gut strangle. There is also rho risk in this, but that is another story...
The other possible meaning of what he wrote is that one of the options is ITM, but both the put and the call are at the same strike. He has to clarify.