Using Lipper or Morningstar, why wouldn't I just select a mutual fund or ETF that is all 5's (Lipper) or 5 stars (Morningstar) as my starting point and then further select based upon the associated fees. It seems Lipper and Morningstar are screening the best funds, from which point, I would select that fund that meets my desired price and has lower fees.
Sure, plenty of people do just about what you mean. (I'm not sure what "Desired price" means, but I assume you mean that it has a share price that is compatible with your desired investment, i.e. if a fund has $350 a share and you have $1000 to invest, you wouldn't pick it since you'd only be able to put $700 into it. Otherwise I'm not sure what exactly you'd mean).
The ratings by Lipper/Morningstar/etc. are not particularly valuable for expert investors, but they add a bit of a baseline for novice investors who don't have the ability to make good decisions based on more information.
The rating isn't all that valuable overall, because it's just a risk adjusted rating of past returns (see article by Morningstar. As you'll read everywhere, past returns are not indicative of future performance, and so a fund that has a 5 star rating in the past might not be good next year. VOO for example is sometimes 4 star and sometimes 5 star, because it's somewhat risky (being an investment in the general market); sticking to lower risk funds might keep you from gaining quite as much in a bull market.
There are lots of other things you should be considering, of course; if it's a taxable account, take into account how much taxable income the fund will generate, for example. If it's an account you want to be able to move things out of relatively quickly, consider how easy and cheap it is to sell shares. You should separately evaluate the risk and volatility of the fund, even though the ratings consider that, and compare it to your personal risk tolerance. Do you want more risk/more returns? Or a bit less? And how diversified do you want to be...