A cpu cooler isn't really all that necessary unless overclocking. That's to be expected though, whether overclocking an i5, i7, fx 6300 or fx 8350. Stock coolers usually handle stock loads though maybe just barely. Again nothing new whether amd or intel under sustained loads such as hours of gaming or rendering. They ship them with a cooling solution that's just enough - barely and nothing more. If in a warm/hot region or climate an aftermarket cooler would be a good idea regardless of the cpu, stock or overclocked.
Agreed though, not enough data from actual z170 motherboards in use to determine which are problematic or not. They should be fine regardless which one you get though asus and gigabyte tend to put out pretty consistently good quality products. If something on the board doesn't work it's covered under warranty which is about all the protection anyone has from faulty hardware.
It depends on what your needs are. The z170-p is a budget z series motherboard and doesn't have as many power phases as the z170-a (which is still a somewhat basic motherboard). That could affect overclocking potential if you plan to overclock. It doesn't have the capability to sli multiple nvidia graphics cards where the z170-a can run 2-3 way sli. It doesn't have as many sata ports as the z170-a. If you don't need the extra features it should work fine for you. Typically features and number of ports for sata and fans etc determine price, the cheaper a board is the less features.