This seems to confirm that there is no functionality to create a seamless experience for the user that actually requires the presence of the web server. If you don't have the client installed the page can prompt you to download it the same as it would the very first time you download and install it. You can ask your browser to remember the link association and not be prompted for which app the link should open going forward. These are minor steps, even for a regular user, and ones with which most users are likely already familiar.
To me this further illustrates that the web server is truly just a ploy on Zoom's part to keep their hooks in users' systems, and have a way in that the user isn't privy to. Any other excuse they are giving about "enhanced experience" is dubious at best and deceitful at worst.