This does work for the use case where you only want to set an initial distribution, but quite often you want to play with trading one option against another afterwards, e.g. spend more on housing and less on holidays, but not less on food or car payments. Basically when developing various scenarios you set an initial distribution (the baseline) and then make scenarios, variations on that baseline. (I imagine it's quite similar for people doing serious exercises with the tool in the OP, I've also written tools to assess investment options, that is similar too).

(The above is a simple example of a personal budget which I always use to illustrate the point, my actual use case is usually something like 'spend more on nature protection and less on road maintenance, but don't change expenditure on social security'. It's easy to see how various political persuasions have some sliders they don't want to budge on, some they want to minimize, and others to maximize).

Usually you need some form of 'reserve' account in your UI; i.e., you're 'spending' from a certain total, and as you increase/decrease some items, that amount is taken from / added back to the reserve. But then how do you guarantee people always spend everything (in some cases that is needed) without introducing modality (i.e., a dialog that says 'you need to spend everything' when you click 'next' or whatever). And sometimes you need a way to move units between accounts, without using the reserve as an intermediate store; plus you usually need a way to move exact amounts, which is hard to do with sliders.

Another approach is something where you stick with the sliders you proposed, and add functionality to 'fix' certain ones, and optionally a way to indicate how much to increase/decrease the others. E.g., proportional to their current values, or distribute the amount equally, or something else, ... The problem with this approach is that it is natural for nerds, but almost instantly becomes unwieldy for 'normal' users. And in that case, the 'fuck it, let's do it in Excel' is better.

If you're interested in this sort of things, I'd love to hear your thoughts or see mockups on other ways you think this could be done. I have talked about this numerous times but usually not with people who know something about UX or even care, beyond their project in front of them.