No - all web apps should be designed with the idea that the client only has a little CPU, ram and storage, and if the user tries to do something outside those capabilities, the server should do the work.
Nobody expects a Google search to involve the client crawling the whole web and picking out your search keywords...
How is that an answer to the question? Your explanation shows how the service is pretty much doing everything which seems to justify why a paid service would be acceptable. If they provided free code but your had to pay the expense of running it locally would be more of a justifiable reason for not finding a need for paying.
Nobody expects a Google search to involve the client crawling the whole web and picking out your search keywords...