It seems that politicians make a lot of decisions that aren't socially optimal because they want money from lobbyists and other campaign contributors. Presumably, the purpose this money serves is to keep them in office by allowing them to advertise a lot the next time they're up for reelection.
So the question then becomes, "why do they want to remain in office?". I could think of two reasons: money and power. From what I know, politicians have a pretty high salary (congressmen make ~$175k), so that's an understandable motivator. But power is the one I don't understand.
Supposedly they want to remain in office so they could use their power to have an influence. I don't know too much about politics, but it seems that politicians spend most of their time catering to lobbyists and voters rather than pushing the things they actually believe in. So much so that they aren't actually exerting that much power. And it seems that most of this catering is to special interests and is socially suboptimal. (I may very well be wrong on these points. I really don't know but it's the impression I get.)
Why are congressmen so motivated to stay in office, make $175k a year, exert a minimal amount of real power, and spend their time catering to lobbyists and making socially suboptimal decisions? I'm sure they could make twice as much in the private sector. I feel like there's something obvious that I'm missing here, but I'm genuinely confused.
Others are probably right that politicians have plenty of genuine choices, where they don't have to use their decisions to cater to lobbyists (or even voters). It's a bit different in the UK, because legislators also form the executive: congressmen may have rather blunter tools to get their way, but Ministers in the UK definitely make LOADS of decisions and a large number aren't fixed by voter demand, lobby power or even party position: working in the civil service supporting Ministers I've seen fairly substantial changes to policy made simply because the individual Minister is replaced by one with a different outlook.
There's also the point that politicians 'cater to' THEIR voters/lobbyists, for the most part. They rely on the support of those that broadly agree with them.
I also think you're approaching this too much as if being a politician is something someone's worked out carefully as a strategy to do a specfic thing. People find politics exciting and engaging - a lot of this, though not all, is because of genuinely caring about the issues - and that's why they want to be involved with it. Once involved, they want to be succesful, that's human nature. I doubt many people go into politics purely because they've calculated it's the way they can get a list of policies delivered, although I think there are a few and they can add a lot to the political process.
Come to think of it, it's worth you looking at other countries if you're interested in this. Your theory of lobbying assumes that individual politicians can rack up $ms of advertising money, but various countries have spending caps (UK) or have systems of proportional representation that mean you can't really advertise as an individual. If you observe the same phenomena without the personal job-security element, then your model is probably flawed!
Your description of why people go into politics has cleared things up and makes a decent amount of sense to me.
I could imagine this sort of thought process. Thanks!