It could also reward you with intangibles or things that change your power orthogonally. Here are a few possible ideas off the top of my head:
Being able to directly access the resting option from the travel screen and the travel screen from anywhere in the keep. Possibly ditto for the merchants. This would allow you to skip loading screens, which doesn't effect in game power in the slightest but would be an incredibly nice feature.
Being able to leave a companion at a structure for a number of quests and respec them (possibly to varying degrees, depending on how long you leave them). This wouldn't change a hypothetical player's power, since they could have theoretically made any of those choices to start with, but it could let them correct early game mistakes or make the game more pleasant. It could also make it easier to try out new builds.
Move enchantments from one weapon to another or strip enchantments from a weapon and salvage their components. This would let you experiment with enchantments more and put interesting enchantments on weapons you're more likely to use, but it doesn't actually give you anything new.
Have the merchants take custom orders for a slight markup (I want a weapon with these enchantments and get me these ingredients while you're at it). This could, potentially increase a player's power, but at least they'd be paying to get the things.
Training room where you can spawn monsters (who would drop no loot and grant no XP) to fight against and test new strategies.
lets add some things up
I like the retraining idea to a point, playing hardcore i find it hard to keep the eight companions around when i can custom make my own. so patching up their lore, mechanics and stealth to make them respective members would be nice so i could keep the unique dialogue around
Leaving members at the stronghold should grant incentive or perk. the adventures are awesome but the rewards arent that great. BUT its a reward with no risk. add some risk... death and dismemberment, NOW weve got some RPG going
Some definition to the taxes and day/turn cycle would be awesome. that statue chair broad could be more helpful, or interesting.
The keep has some awesome potential for RPG drama, like trade routes, discontent, famine, plague, WAAARRRRRR! mmm building an army.... that one a**hole hung half his town from a tree, ONE TREE! the most i can do is butcher my people...
i agree it shouldnt be a source of income but definitely an investment for immersion. id pay to have merchants with unique quests for their great gran dads war relic or whatever, their MY towns people, give them some personality! or at least let me hang them... i can buy a tinkerer but wheres my gallows and giant scary executioner???
fixing the battles so they arent inside of my keep would make sense since i built giant walls and towers- could put those to use
thats off the top of my head, feel free to add. man i so want to buy a hanging tree for my town. a burning post. some of those torture racks would keep the public in line...