The issue with that is that with "what's the best for the country" is not an objective value. I know I believe that a reduction of government influence in many matters would benefit the nation, but there are others who DEFINITELY disagree with me (I had a few incredible discussions with a self-proclaimed authoritarian), and that's where democracy comes in in the first place. Short terms hold officeholders accountable to more than just their own definitions of this value, which would blow over dissenting voices with even greater efficiency.
Incidentally, the existence of Congress GREATLY GREATLY safeguards against tyranny of the majority, with voices for SEVERAL groups that would see very little sway otherwise, like the mountain states. The ability of congressmen to slow presidents down because they have to to get elected prevents the presidents from ignoring the voices that didn't vote them in.
Yet individual congressmen don't actually need to represent their voting district; just their constituents, because Winner-Takes-All style voting system. I'm not saying 'install X person and he will run the nation perfectly', I'm saying that if we had a single person who was genuinely trying to make the country better, was genuinely intelligent enough to go about doing it competently, and genuinely motivated enough to look into stuff about what policies cause what effects, or knew it already, you would be able to avoid a lot of the problems with democracy. Yet it's still the best we have because trying to get the perfect guy to be Supreme Leader, and trying to make sure he gets fed true information that isn't biased, mutated, morphed, nonrepresentative, and so on, is essentially impossible, so we're stuck with trying to do an amalgamation of the two methods which is having a democratic republic, and hoping we can elect people who are competent.
The problem with short terms is that it's susceptible to mob rule and means the politician is trying to do their job in order to keep their job, rather than keeping their job in order to do their job. And even if they're trying to simply do the best they can, if they make a mistake and don't spend their time covering their asses, they won't keep their job, and now you have someone else who's probably less concerned with actually doing their job correctly!
The problem with long/life terms or difficult to impeach people is that it's really hard to hold them accountable for their actions while they're in there, and their values/practices might change from what made them qualified in the first place
The problem with unlimited number of terms, particularly if short, is basically all the problems with short terms, plus they get more and more skilled at politicking, so the problems with long terms show up but still nothing can be really done.
The problem with single terms is that when you have a guy who's actually competent, he might not get the chance to stick around and get anything done, and you don't have much of a way of telling beforehand if they're competent, and if they were, they're about to replaced by someone else anyway.
Problem with winner-takes-all democracy is that it means you don't have to care about the rest of the people you're meant to represent. Problem with voting districts is that you don't have to care about anyone else in the country, period. Problem with not having voting districts is that people can't self-determine for their locality; and of course there's the general problem with solving these problems of having to care about other groups or areas at your own expense, determined purely by who got the most votes and tyranny of majority problem again.
So maybe the two-term thing of eight years actually is ideal, and we just keep screwing it up because we're still humans and thus flawed. First term means you have to actually have people supporting you, and be held accountable, but you still have enough freedom to lay the groundwork for your next turn, in which you don't have to worry about being elected again, so you can actually (try to) get shit done.
Huh. Somehow writing this post increased my hopes and confidence about America and it's government system, where it started off as a lament of democracy being the best we have yet still sucking. Weird. Now we just have to get Congress to function on four year (or possibly six, but four seems about right) two-term-max intervals, preferably offset to presidential election years....