Reloading, reliability, cost, and power.
You can't reload rimfire cases without special equipment and without handling quantities of raw, explosive priming compound. Not fun. And, reloading a rimfire still doesn't iron out the indentation on the rim. You would have to, on subsequent loadings, orient the rim properly or have a misfire.
Reliability Fatcat has touched on.
Cost is the fact that it takes special, and expensive, equipment to fold the case heads.
The power aspect comes from the fact that folded heads, by their very nature, have to be thin to allow the firing pin to deliver a sufficient blow to detonate the priming compound. In today's high-intensity rounds, the thickness of the hollow rim would have to be extreme to contain the pressures.
And, generally, another consideration is that many of the rimfire rounds never proved to be all that accurate. Why, I'm not sure.