I second parts of Frankie's answer here but for a different reason and with additional caveats:
First yes, do not run a process that does not serve content you already provide as a web application. The point of a web app is to simply make content available on a standardized medium for distribution purposes and not for computational or data gathering purposes.
I have seen people implementing a whole strategy testing and trading platform on a web app, which imho makes zero sense. Its a very inefficient and prone to error process. The point is that if a single of your computations goes down it essentially renders the whole web app useless. The correct way to run this is to gather your data through the API on a server or local machine (whatever you prefer) and to then offer the gathered data (raw or cleaned or otherwise processed) to users through a web application.
You actually answered the question yourself, you often need other processes that run in order to gather the data you inquire and you don't want to have to mess with this on a web app and or even worse force the user of the web app to run other processes just in order to make it work. Gather the data on a machine, process the data, make the data available through a web server and use the web app as interface. Simple as that.