Your opening premise, that being a naked put write is a strategy which is a bet on price remaining stable or rising, is, I believe, an incomplete (and therefor inaccurate) description of an uncovered put write.
Many people use the uncovered put as an investing strategy to acquire stock at a better price then where it is currently trading. For example, they may feel they would like to own stock ABC, but think it may be overbought at its current price of $50 share. Based on their analysis, they may feel that acquiring ABC at $45 a share would make more sense. They could leave a limit order with their broker at $45 or they could (assuming t hey have the proper option trading permissions) write an uncovered put on the stock with a strike price of $45, They would receive a premium for writing it, and hopefully the stock would fall (albeit temporarily, after all their analysis makes them want to own the stock at $45) to below $45 so it would be put to them at $45 (their cost basis then being $45 minus the premium received for writing the put). If in fact the stock never drops to $45 by the expiration date of the option written, they would not be assigned the stock, but of course would keep the premium anyway. They could then rewrite the put at whatever strike and expiration they thnk is an appropriate acquisition price and start the process anew.
To me, if you are going to be using an uncovered put write, one of the first things you need to have established in your analysis, is that you would not mind actually owning the stock at whatever strike price you wrote it at, after all, by writing the put, you have already effectively bought the stock and sold a covered call at the [put] strike price, since the 2 strategies, covered call, and uncovered put write, are synthetically the same, with the same risk/reward profile.