Clearly they can, they do.
But personally I think they should be paid more, both to improve the quality of people who do they job (lots people who would or did make great MPs are off doing other jobs, paid 100ks more, for a far less demanding life - even if the other job is as tough, far less public scrutiny, which is what you signed up for, yes, but very hard on your family).
And to ensure that anyone, from any background, could do it and still live their life (e.g. provide their children with a stable home). 60k is not a massive salary for central London (where living costs are v high and MPs must be based at least 4 days a week) and then they have to spend time in their constituency too.
Throw a family into the mix especially with young children, and its a job that it just unaffordable for many. And that's before you consider whether, on its own terms, its reasonable compensation for the crazy demands of the job (on call 24/7, your personal life and family life alwas open to public scrutiny).
This combines to mean lots of people who would be great MPs consider all of that and just think: 'no thanks'. And especially if they don't have money from some other source to make it possible. So this problem discriminates against those that don't come from money far more than those that do (e.g. David Cameron). And, it drives corruption.
As with everything in life, you get what you pay for. I think the quality of MPs we have now reflects their level of pay. So poor pay = poor MPs.
Globally they are massively underpaid. American Congressmen and Senators get 200k ish I think, plus other perks. MEPs get a package worth more AFAIK.
I think we should pay them a lot more (200k+), but then have a ban on them having other outside earnings while they are in office. There must be a way to manage investments etc as distinct from earnings for work carried out. They can work it out for other significant public sector appointments e.g. head of regulators etc. Although where their was a notable conflict they'd either have to declare or divest. And likewise a ban on working in related sectors for a while after they have stood down. If well paid all that is ok.
Also, we should get rid of the expenses for second place of residence issues. The State should provide them with somewhere to live in London while they are an MP (so like their office, you get the use, but don't own it). Then cost of living in their consituency is their own affair, no State money goes to it.
it would clean up a lot of these scandals and broaden the range and number of people who could / would be MPs.