I wouldn't know about IB Maths being a joke - I'm finding I know so much more than those who've only done A-level maths and further maths. And I haven't had any problems doing mechanics at uni even though I haven't done IB Physics, while several of my colleagues who have done A-level physics AND mechanics in maths are struggling. I think this has a lot to do with IB maths being a superior course ...
And there is a subtle difference between saying that there is a lot of maths in mechanics and that mechanics is a part of mathematics.
Mechanics is quite mathematically demanding
physics. Incidentally, A-level physics is ridiculously easy in terms of the maths proficiency expected of you: you're not required, I'm told, to be taking a course in maths alongside, so it needs to be stripped of all the fun mathematical parts.
I don't see why you would want to have applications of maths to physics in maths rather than in physics - especially not if, when you want to take physics in the IB, you need to have a Group 5 subject, ie maths, in any case. Maths as a subject should be, I think, about proof and other fun things like that, not just applying it to solving some physical problems. Not having mechanics in maths enables you to do lots more in terms of pure maths - which is, in fact, harder maths as well. And you know it's all perfectly true in a mathematical world, rather than an approximation to the real world. That's what makes pure maths so beautiful, I should say.

And also, it is possible to do A-level maths without taking any mechanics modules. I don't see then why not having obligatory mechanics in maths would make you lose respect towards IB Maths?