A strong argument against shorting puts as a way of starting bullish exposure in my view, is the following:
You might not necessarily buy a stock if it goes down to the price you thought it was cheap because there is new information avaliable
If BP goes to $25, I would not jump in and buy it. I need to see why it is there, if its there because estimates of losses are growing, I would try to see if the analysis is wrong, if it is I buy it, if its not I dont get involved. At $25, there is something wrong with the price, its just too much of a steal, which means there is a catch and I need to find out what is it. The market does dumb things but when the money is too easy, I dont want it, at least not yet, the market is likely fooling me and there is something I dont know
This could apply even to stocks like Berkshire Hathaway, if you can buy BRKB shares at $20 a share(down from $70ish), there is something wrong(perhaps massive accounting fraud), you might not want it anymore
The solution is to take that into account and put the probabilities of such event in your calculations then see if the premium is big enough to compensate for those risks. And of course, being conservative in the position sizing