I think in social sciences it maybe more of an inability/reluctance of the domain group to use the mathematics as opposed to the mathematics being absent.

Take category theory for example. The initial mathematics appeared in 1942. The application to social sciences started in about 1970 and I’m not sure of the level of uptake at the current time but a quick AI search says applications have accelerated in the past decade (needs verification).

What open problems in quantitative social science do you have in mind where better math could achieve massive improvements? I'd expect the bottleneck to be data availability nearly always.