Each page is machine readable: https://grid.ac/institutes/grid.5335.0 -> https://grid.ac/institutes/grid.5335.0.json (other formats work too, like nt for triples, and accept headers can be used instead but I can't make those into a link).
So if you count that as an API, we offer it because the whole project is about getting people to use persistent identifiers for research institutes and using that in their workflows. Free an public data is required for this to work well, and making it easier to hook into your processing is vital.
Selfishly, if people used persistent IDs more then my job and the work my company does would be significantly easier, so giving people a free way of doing this and making it as easy as possible for them helps move the field I'm in forwards. Also, when we have grid ids in our data outputs, we want people to be able to use them & get extra metadata. Making our own products easier to use & integrate adds value as well.
Edit - you can see others using the ids here:
http://www.bookmetrix.com/detail/book/2062f9b3-4e4f-4f00-b79... under affiliations
They're in the Altmetric top 100 lists https://www.altmetric.com/top100/2016
Linked up in scigraph: https://github.com/springernature/scigraph/wiki
It's used in wizdom.ai's visualisations https://wizdom.ai/public/analysis/brexit/dashboard?chromeles...
They pop up elsewhere too, but those I knew I had the links to handy.
People collect much stranger things than public APIs :)
Someone needs to make an open API to query a list of open APIs
At the very least, lists like this should be maintained in json. Worst case, you just pull for an update and the wrap that in whatever you want.
And for the repo just use gh-pages to display the json in some human-friendly format.
I've always want to build a Quora-esque app for public lists. For example, you could ask a question, "What are the top things I need to know about X?" Other users can post answers, as well as up vote and down vote. But something KISS. Not long full answers (a la Quora) but short and ideally with a link. So a list of high quality links in response to some question/need.