Put options lose value over time. You are speculating on the near-term risk of stocks losing value - effectively trying to time the market/predict the weather.
Selling put options is a bet that the put options will expire worthless, which is a bet that stocks will continue to go up/not fall.
I honestly believe the insurance analogy for options is misleading. The value of an option is quite literally the difference in value between selling the stock at market price and at the option strike. As a stockholder you don't save yourself as much from buying put options regularly as you would from say getting a surgery covered with health insurance.
I do something like what you are saying but with selling covered calls while I am long a stock. A quick search online will show you strategies like this. It is not uncommon for more active equity traders.
I mostly play long cycles in the equity market instead of trading. When I do trade equities, I play one or two stocks that I know their behavior intimately. My very active trading is mostly in futures and currencies.
Yeah, thanks to put call parity a covered call and a naked put are basically the same thing. (I wonder if it's in some more general sense similar-ish to lending out your long equity to short sellers?)
Having said all that, I'm an indexer at heart, and working for Bloomberg I'm not even allowed to trade the more interesting stuff.