I have some comments, which I will post in form of questions to stimulate thinking. The first comment relates to cash secured puts. If vol goes up (even if market does not move), then the short put would require more than the cash for the given strike. Therefore, selling a put is never cash secured between the beginning of the trade and its end, even if it is secured at the end...
Short the put is also short volatility. If you have closed out by your brokers, it may happend when bid ask spreads are wide (very wide).
Riskfree,
I think that you're getting lost in theoretical possibility versus practical reality with a touch of extenuating circumstance (g). Here's my take on your scenario...
In order for the put's value to approach the value of the strike, volatility must go up into the 1000's. That's not going to happen especially "even if market does not move". The other possibility is that the stock drops close to zero. In both cases, it will approach parity and will only trade above parity due to the spread.
Suppose the stock is 50 and you're selling a naked 50 put. Parity can be no more than 50. Now how wide will 1/2 the spread be? Will a $49 premium (stock at $1) go to 45-55? 40-60? Possible but very not likely, even in a crash. Long before a $50 stock hits $1, assignment will occur or we'll all be glowing.
And even if these wild/wide premiums did occur, my assumption is that it would not matter since the options price for margin calculation would be the average of the bid and ask which would at worst be parity (that's how my broker determines market price).
There is a theoretical situation where the short put would require more than the cash for the given strike but that assumes that you're going to be in the above situation where the stock loses most of its value and you're not assigned.
Consider a naked 50 strike put when the stock is $1. Assume that it's at parity or $49. Margin is 100% of option proceeds plus 20% of underlying's value. However, this position gets snagged by the minimum requirement which is the option proceeds plus 10% of the strike ($5400). Since the premium can be applied to the margin requirement, the margin call is $500.
Now if you sold this put when the stock was $50 , at $1, you didn't receive the $49 premium to offset. You have the premium received from the sale. Say 2 pts. Since the requirement is $5400, you're going to be $400 away from cash secured ($4800 + $200 premium) which is your premise. While this is theortetically possible, I think that in reality, it's just short of impossible.
To come full circle, your broker isn't going to sell you out if you have a cash secured $5,000 and $400 of margin.
As for your suggestion to "never sell the put, but rather implement it as a covered call", that's a whole nuther story because although the risk profiles are equivalent, the margin profiles are not.