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.
Yes you did miss something......Buying power will drop a lot more than any credit you receive, so you are "tying up cash" when you sell options.
That's called a guts strangle. It's risk/reward is equivalent to selling the same strike OTM strangle. However, it has several disadvantages. ITM options tend to have wider spreads and don't trade far from parityand are therefore more likely to be exercised early. Also, the margin is greater for the ITM guts strangle than for its OTM equivalent... I think maybe double. I don't know where to begin with that one. It doesn't matter what the market price is when the option is exercised. It matters what it opens at after you are assigned. You will be OK as long as the underlying isn't outside the strikes by more than the total premium received less the difference in strikes (for the guts strangle). Not true... see above.
Margin point is in my post. I did not miss that. And the answer to your point on margin is it depends on other things (rest of position, how margin is computed, etc). Here is an example. If you hold a long strangle position (OTM) and wrote against it a shorter term gut strangle, the risk profile if not assigned earlier, is the same as if you were short the OTM short strangle. Depending on how your broker views this, there can be no diff in margin. If so more cash will sit in the account of the writer of the gut. The interest stuffed in the short-put side may however work a little against the gut writer, but is hedged with the interest earnned on the intrinsic value from the value of stock to the short put. Also assignment can turn your overall position upside down (read post by Spind0 in this thread) If you think that buying a gut strangle is not a good idea, don't you think that the other side may have something to gain even if the other side is 2 different traders?