A lot of it depends on why the system is buggy in the first place and the relative strength of the DBA within the organisation.
It might be that the management either prefers or is obliged to update the system in «patch-mode», that is, continually applying a myriad of small fixes rather than being able to make a fully-tested release or update once or twice a year. If this is the case, the poor DBA is being called upon to counteract the symptoms caused by the problems of poorly-tested patches.
One recognises that occasional events will cause one to go to work during the holidays, but these must be occasional and extraordinary. I define occasional as once every couple of years. If you are explicitly needed during holiday time, they can discuss it with you well in advance and reward you as appropriate.
If the DBA has a strong position and would rather be at home with his/her family during the holidays, they can say well in advance, that they will not be available during the holidays (as management tends also not to be available).
On the other hand, if the DBA's position is weak, he/she should use their time well to see how a company & a system is run badly and start looking for a new job. I have seen too many instable systems go down too often and anger customers. This is a warning.
Young DBAs (without families) who don't mind being constantly at the beck and call of a buggy system during holiday time should benefit in several ways during holiday time. As above, you learn how a company & a system is badly run and look for the warning signs in the future.
Secondly, if you have the time, the inclination and the necessary permissions, you can find out what actually is going wrong. You will usually be impeding on somebody else's territory and, if your solution has demonstrable benefits, you will look good (assuming you go through the right channels to get it applied) but others will look bad.
Thirdly, you will learn a lot about broken systems and how to fix them. This knowledge and experience is invaluable in the future once the shit has hit the fan and solutions are needed quickly.
If you do work during holiday times, you must be sure to get the acknowledgement that you have done something over and beyond what is accepted as normal and be rewarded commensurately. This may be financially, with extra training courses, with extra holidays (you may want to take a 5-week holiday in Thailand, for example). And make sure that you capitalise quickly on the goodwill garnered by your working during the holidays. It may not last long and management may rather get to like the fact that your solving problems whenever they arise makes life very easy for them.