Lipos are pretty darn cheap as it is, considering life span, current density and so on. I don't think you save enough with "cheap" to make it worthwhile. Panasonic 18650 batteries have served me well in high-drain flashlight applications and they cost about $7 US each. If they are good enough for Tesla, I can't compete with their research. Current ratings are all over the map because there seems to be no standard test conditions and that makes all the difference. You do need to invest in a quality charge controller with a hard cutoff and well controlled current. Still, sleeping with a phone under your pillow is a good definition of insanity, with or without protection circuits.
If you ever had to put up with the short life-span of NiCads...they were really a rip off. Battery powered drills and other tools were a bad joke. The batteries would crap out in short order and replacements cost as much as a new drill. I have had an LG flip-phone since before Noah's flood and it's lipo is still trucking. Even the original lithium pack on a Compac Presario sold just before the turn of the century was still good until a few years ago. The cost of a battery or pack is nothing compared to the cost of the circuitry it drives and the time and effort that went into the project.