> Why would someone elected to office, who knows they can't run again, have any concern about the will of the people?
Reason #1 is the Princeton study cited in other posts:
> The key finding: “The preferences of the average American appear to have only a miniscule, near-zero, statistically non-significant impact upon public policy.”[1]
It's already clear that "the will of the people" isn't being represented currently.
Reason #2 is "the will of the people" being reflected is not (and has never been) a design goal of the U.S. system of government. The U.S. was specifically created as a "representative democracy" and not a "direct democracy." This was debated extensively at the time of the founding of the country. They decided then (I think correctly), that it was better to have voters choose representatives, who, once elected, are supposed to vote what they personally think is genuinely the 'best' answer, not what they think 51% of their district's citizens want them to vote.
> they could spend their whole term making money for themselves with no concern about re-election.
This is already super against the law and congress members have gone to jail for it surprisingly often. The FBI has a special unit constantly searching, investigating and probing for any sign of it. At the same time as single-term limits, I would >10x the budget of these investigators. At least enough to ensure that more than one lobbyist meeting a year per legislator is a well-run Abscam-like sting operation and the politicians have no idea which one. I'd also substantially increase the jail time for such convictions, along with substantially increasing our one-term legislator's pay at least to $1M/year. The goal being to reduce the need to cheat while dramatically increasing the penalties for cheating.
Combined, the higher pay + higher penalties would have the effect of significantly increasing the $Cost to influence a legislator with money. While the single-term limit would greatly reduce the $Value of influencing a legislator. Having the ear of someone likely to be in power for many terms is much more valuable than having the ear of someone who's gonna be gone for sure next term. I think the combined result will substantially reduce the amount of illicit influence peddling, leaving our legislators free to simply vote their conscience - which is really the best result we can realistically hope for anyway. None of the "Suspiciously Got Very Rich While in Office" >5 term legislators accrued any significant wealth in their first term. Even with the current laws, penalties and underfunded FBI enforcement, the only way to get rich in congress is to do it over many terms.
If you really sit down and thoroughly ponder how single-term limits would actually play out in the real world, vs the results we are actually getting now (not what we should be getting), there are a lot of interesting impacts. For one, it's very likely to reduce the power of the two major duopoly political parties who've jointly controlled Washington for >50 years. While it would increase the viability of tertiary political parties who are currently irrelevant. It's also likely to increase incentives for tertiary parties to sometimes form meaningful alliances as we see in some European countries. Anytime anyone votes for any candidate OTHER than a Democrat or Republican, it's currently a wasted vote. Thus alternatives can't ever build any gradual, grassroots traction and things just grow increasingly polarized at the extremes.