Software that does not run in the browser can do even worse things (that are not possible in a browser): it could access (and upload) arbitrary files other than

Software that does not run in the browser can do even worse things (that are not possible in a browser): it could access (and upload) arbitrary files other than just the PDF file(s) you gave it access to, it could set up things that stay running even after you close it (like a virus or keylogger), etc — so you need to verify/trust the developer or run it inside a sandbox, and the same is true for in-browser software. At least with a browser, the tools needed for monitoring and disabling network access (dev tools) are built-in to the browser (e.g. don't have to separately install Little Snitch). One thing that seems worse with software-on-a-webpage is the risk of malicious behaviour getting added later (this is also possible with non-browser software with automatic "updates"): you could mitigate it, if you trust or have verified one particular version of such a webpage, by saving the HTML file (put it in a Dropbox folder say) and opening the file (maybe with network disabled), whenever you need to use it. But then you lose the advantage of "don't have to install anything"; it's a trade-off.