Actually air refueling and ILS's are among the most stable flight operations I can think of. If you've ever seen an air refuleing operation in progress, they look like two parked cars. What was really something to see, was an air refuling operation coming at you head on! While you're doing it, you have very little sensatioin of speed. However, viewed from a distance with some closing velocity it's quite a site!
The tanker pilot, sets his power and speed at 255 IAS as I recall. Once you get through the bow wave and stabilized there's very little throttle jockying that takes place. In fact, to make my point to students, I often demonstrate a "Look Mom, No Hands" type of contact. My point was to demonstrate the inherent stability of the operation.
On ILS approaches we used to place bets on who could keep an airplane trimmed up the longest from the FAF inbound. We'd hack a clock crossing the FAF and go hands off. The winner was the one whose airplane was stabilized the longest. (10kts, 1 dot left or right up or down). I found these little contests, increased confidence and flying skills. If you're pumping the power up and down final you're having a bad day or you need to review the basic of pitch and power flying again.