The difficulty is that there is a downward spiral: if fewer talented people enter the public service or politics because it is becoming relatively unattractive, the average performance of that class goes down. That makes it harder to justify any increase in salary or other benefits, reinforcing the dynamic.
The reason to avoid a monetary reward is not that it is tacky, but because money can easily be used to pass on influence to offspring, such as by boosting their profile, or buying votes for them. This can undermine a selection mechanism where they should win or gain reputation by engaging in pro-social activities.
Also, not everything may be monetised. I cannot sublet the garage attached to my apartment for example, because the contract forbids it. AirBnB is banned in some cities/situations.
Doesn't seem like a solution to me.
Public service attempts to do this with stability and benefits. In other words, in exchange for power you are promised a comfortable life. This used to work but no longer does because property prices near desirable cities, where the bureaucracies are located, are increasingly unattainable even to well paid bureaucrats. The military gets around this, with much lower pay, by providing lodging for soldiers. Perhaps we should do the same for bureaucrats? The revolving door would have less appeal if you didn't need to plonk down a million dollars to live in Bethesda.