An issue is that understanding itself requires expertise in so many of these fields. I guess that's what makes bio and math different. In bio, the difficulty is in the techniques and the details, but the concepts are simple. On the other hand, in math, much of the difficulty lies first of all in grasping the concepts.
I know much more (relatively) about how the basic objects a biologist studies works (transcription, translation... epigenetics, action potentials, etc...) than a typical biologist might know about circuit complexity and probability theory and quantum physics.
In bio, much of the difficulty is in the details (names of particular proteins, viruses, organic molecules) and techniques that requires years of training to truly come to terms with. But the overarching idea for how these things work and how research works--that's something that's easier to grasp.
On the other hand, in math, a layperson - heck even a math PhD in another field - would have trouble even understanding the rational behind the questions being asked.
Parallel this with how research works in these two fields
In biology, you're able to have much more of a hierarchical structure. Almost like in an engineering domain. You have the leaves (the bio students standing for 10 hours at a lab desk), then the level 1 nodes which are postdocs who have their own ideas for projects to work on, then you have level 2 nodes which are the professors and heads of labs who have certain overarching directions they like to pursue. In industry, then you'll have maybe higher up executives who dole out funding... Similarly, in academia, you'll have bosses and NSF who determine the winds of research.
In math, you also do have significant structure, but this structure is more bottom up rather than top down. It's been sort of dictated by a decentralized process whereby certain subareas of emerged, and people aggregate in these certain subareas and ...........
Though of course, you do still have to ask for funding and there are still people in the field who have a disproportionate amount of influence.
But I would argue that this is different from biology, where the people deciding on funding themselves have their own agenda, while in math, the decision of people providing funding are much less driven by their own, unique, agendas, and more by a sort of group level consensus as to what's interesting or not interesting