I don’t believe this is true.
And being a member of Congress comes with some high expenses. That’s why there’s such a big temptation to accept “gifts” and engage in illegal money-making schemes. Many members of Congress get rich after they retire and accept a job with the industry they’ve been regulating while in office. Dick Cheney for example.
As I understand it from most commentary, it’s in the Senate that a majority have significantly high net worths on their own right; in the House it’s more common, specially with freshmen, that though hardly what is called “working class”, a reliable paycheck is welcomed.
Mainly, the expense of getting elected and re-elected.
Those expenses are handled through separate system. The question asked is why members of Congress would need to have personal salaries.
There is the expense of maintaining two households, one of them guaranteed to be in one of the country’s most expensive real estate markets.
There is the expense of regular travel to visit family or “keep in touch” with the constituents.
Failure to keep up with either of these things is guaranteed to lead to charges of “he’s not really a resident of the district he represents!”
Single-subject rules in state constitutions are easily, and frequently, sidestepped by legislators who really, really, really want to pass this or that bill. And budget bills are usually exempt from the limitation, either explicitly or by court interpretation.
I doubt anything would change on Capitol Hill, alas.