I generally want an almost complete TRM too. In my experience there are many more SoCs with an available TRM than with complete support in the mainline kernel. By the way, there some WIP work for getting RK3188 support in mainline. It can boot but only a small part of the peripherals are supported.

You can never get a complete TRM for high performance ARM SoCs because they all license some IP for which they can't publish the documentation, usually for 3D accelerators and video decoders. You can find leaked Allwinner and Rockchip TRMs, at least for Allwinner A20 (the one used by Cubieboard for example) and RK3066 (which is quite similar to RK3188), so it's a compromise I've accepted in a few cases.