We have many Applications (~100?) to create and Many Access profiles to assign to those applications…(~1800 access profiles or so)
We have created a bulk way to create our Access Profiles, and just now started looking for how to attach those access profiles to Applications.
Surprised and Disappointed to hear that this is not an API.
I am going to need armor when I tell my team the plan is to do this manually. 
Hoping there is a better recommendation.