I really like this idea, but it probably shouldn't work from command, otherwise 5 cost cards would be available turn 2.
Alternate fixes to that:
-Cannot be commander (would ruin uncontrolled rift decks though)
-Unique (I'd rather not, and the card would probably end up pretty bad then)
As for the remarks regarding how the effect would stay in that case, further possible edits to the suggested text:
-Exhaust: If wealthy noble is in play at the start of next turn, you have one extra resource.
(If you change it to read deployed at the start of next turn you could still get a turn one benefit from a command noble, but a lucky draw doesn't add much. Which sounds fair to me at least)
-Exhaust: You gain one resource for next turn, if wealthy noble is not deployed at the start of next turn, you lose a resource instead.
(This one would certainly add to the mind games, but the side effects of losing a noble could get pretty harsh)
Yes you could get a turn two 5-drop, but which one? Immortal Traveler? Martyr Golem? Silfurstar? None of these seem to put an awful lot of pressure on your opponent. Perhaps there would be a case for sacrificing one or maybe even two command slots for extra resources, but I doubt factionless decks would suddenly run rampant.
My problem with this idea, as I mentioned before, is that as a player you are practically forced to activate all your nobles every turn. There is almost no drawback to activating a noble, so logically you always should. Imagine Bloodthirsty Dead had it's ability changed to "activate: Bloodthirsty Dead had Bloodthirst 4 until the end of the turn". It would be incredibly annoying. It's a passive ability disguised as an activated ability.
I was thinking more along the lines of quickly multiplying militia but eh, 5 cost was just an example.
As for irritation purposes, they could always just have it as a toggle or something.
Or to elaborate further, possibly something like:
Exhaust: During each following turn while wealthy noble is deployed, you have one more resource.
If noble had a side effect from being killed (aside from dying, which is a pretty nasty effect for the noble in question as it is) then there could be an option to re-exhaust the card to remove the ability again. Which could add to some fairly fun toying around.
Alternatively in more silly suggestions that should never be implemented:
Exhaust: For each following turn that wealthy noble is in play, you gain one additional resource. When wealthy noble dies you lose morale equal to x*x and a funeral yacht with x/x appears in your support zone, where x is the total number of resources you possess.
When you reach 10 resources wealthy noble transforms into a 20/20 unstoppable flying dragon with money and moves to the assault zone. Money gives the opponent resources equal to half the damage dealt to their fortress (rounded up).