It would be practical to do that, with a few tweaks. Say you're elected to state-level Citizens Assemblies, like Jurors, and shorten the time-frame a little. 4 years might be too long, 2 years too short. And you want overlapping intakes, like the Senate. So ... make it three years, with 1/3rd replaced every 12 months.
The Assemblies then select people to represent them at the state-executive and federal levels. You'd have the regular Assembly members who are appointed for their single-term, but make it so that if you're chosen to serve in the Executive or Federal level, you can serve longer with a vote of support from the regular Assembly members - this way truly talented and dedicated people can be held onto for longer. However, since the state Assemblies are refreshed by lottery on a frequent basis then the chosen Federal or Executive-level people must keep proving their worth: they can't just rely on cronies to keep them in power.
This certainly couldn't be worse than what happens now.
The main virtue I'm thinking of is incorruptibility. With someone chosen randomly and thrust into the position of power, they could perhaps be corrupted after-the-fact, but it sure removes most of the mechanisms that incentivize corruption, or allow it to happen at all.
Actually, scratch all that, how about this: We keep our democracy exactly how it is now, but we add one rule: after the President's term is over, they're mandatorily executed regardless of how bad or successful they were. Perhaps pointlessly cruel, yes, but now the position is one of pure self-sacrifice; and even the greediest, most corrupted narcissists won't want to be elected, it'll be one of selfless civic duty to your fellow citizens.
I'm obviously joking, but it seems we live in an age of extremism where things like this seem sane and sensible.