Entirely feasible. Also reasonable for you to pay me for the service as it is taking my development efforts to meet your business model. The advantage to you is you have a defined interface that I won't prevent.
I guess you missed the comment I was replying to: it may cost you more money, in bandwidth and per page resources, to not provide an API than it does for you to provide one.
So no, I won’t pay you for the privilege of you saving money.
Who pays for that API and the bandwidth? What’s in it for the data provider? On LinkedIn, viewing the data now shows ads or at least prompts the viewer to join the network. With scrapping and free API access, how exactly does LinkedIn benefit for their work of hosting the data?
Unless the costs exceed their current operational costs. Don't forget the time spent redeveloping on the new API, which includes validating everything is there, testing and cleaning up and removing the old (working) code.
This isn't a great analogy here - getting the data delivered via API is simply more useful than having to re-assemble that data out of fragments parsed off of different web calls.
Could I suggest:
"Why buy the cheese when you get the milk for free?"
Look, if you build a product that relies on providing free information to the public, then you don't get to select a segment of that public and charge them for it. You can't hang a billboard on a highway, but then get upset when some people look at it the wrong way.
Now, if you want to have a walled garden and charge for entry to some and let others in free then that is fine.