The only reason one would write Puts is if you actually believed that the stock price would stay above the strike level at the time the options expired. If there is no mechanism to take the price down then of course you would write Puts.
I assume that there are enough Puts already out there (that can be purchased and exercised) that writing more isn't an issue? Those Put writers may get rich if shorting is not allowed. But once shorting is turned on again it could be a mess for them?
Once shorting is allowed again you wouldn't want to write Puts you would want to buy them. And who is going to be long once shorting is allowed again since stock prices will be inflated?
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