I can’t really help around medicine requirements other than saying what the previous two posters have said sound right from what I’ve heard.
But regarding why they do an EPQ - there are quite a few reasons:
There are a number of uni courses for various subjects that include it in offers in some way - in that a very good EPQ means you can drop a grade in one other subject. For instance this sort of thing from Birmingham: https://admissions.bham.ac.uk/knowledgebase/article/KA-01332/?level=undergraduate
Or if your offer is made on ucas points, like one of my son’s friends, the EPQ comes with ucas points so it can help make up your required offer.
(It isn’t necessarily the case as well that “if you’d not done the EPQ you’d have got higher grades in your 3 subjects” - maybe for some but for others it’s more about spreading your bets, and adding in something that is entirely coursework rather than relying totally on a short time period of intensive exams).
It can help build interest and “personal statement material” in a subject you’re applying for, that isn’t directly linked to one of your a levels. Eg one of my son’s friends was studying something like history, eng lit and maths, and was applying for law, so he did his EPQ on a law based topic.
The EPQ also teaches them v relevant skills for uni / life - doing a biggish piece of research, documenting it, drawing conclusions and writing essentially a dissertation. Even if you don’t need the points / grade for anything, this can be a valuable skill to start building.
But like you say, it does depend a lot on what the student wants to go on to do. My eldest was going on to engineering so it was a no brainer for him to do further maths a level instead. My youngest is thinking about law and while he’s very capable of doing FM a level, he is sure he doesn’t want to go in a maths-based uni direction, so is doing an EPQ to build his dissertation writing skills and get some law type research under his belt to add to the other law type things he wants to do for applying that they need to do to be competitive.
It sounds like for either your DD’s options of maths or medicine, it wouldn’t really help to do an EPQ - for maths definitely the FM would be a far better choice. And for medicine I don’t think the EPQ is as helpful for anything - I think that medicine entry reqs don’t tend to lower entry requirements with epq as much as other courses. Though do check that - just something I saw in passing.