You are right that the FCOM does not shed much light on the RTA function. Based upon my own observations over many years, I offer the following:
The B777 has a 'supercritical' wing, which means that it is efficient within a limited range of mach numbers. This range is approx 0.815-855 M. Above and below these values the induced drag rises very rapidly. I believe that Boeing set the RTA values within this range to keep power required, and hence fuel burn, within sensible parameters and to also keep you away from high or low speed buffet margins. If your required RTA cannot be achieved within that speed range, you will get the 'unable RTA' message. Of course, you can set your own very high, or very low speed, to make good an ETA but you would be choosing to erode the buffet margins and substantially increase your fuel burn.
Standing by for technical explanations.......