Assuming that a relationship is monotone sounds like a very strong assumption, and therefore one that you’d expect to gain a lot by making. Asymptotically, this isn’t true.  If the relationship between $$X$$ and $$Y$$ is only known to be monotone, you get $$E[Y|X=x]$$ estimated to $$O_p(n^{-1/3})$$ where $$X$$ has non-zero density. By assuming smoothness you can get $$O_p(n^{-2/5})$$, which is better. That is, if you have a lot of data and you know a relationship is smooth, you don’t gain anything by knowing it is monotone, but if you know it is monotone you do gain by knowing it is smooth.