Deployment is definitely harder, but not to the point where it's unmanageable. Click once is one solution that's very common, though not great. It will check a url for a new version at startup and install that version. This URL can be a simple aspx page that gives each user the right version, I recently automated this as part of our CI deployment.

A better solution would be something like chocolatey (https://chocolatey.org/), which is basically a package manager for windows. It doesn't do the automatic updating, but doing that with a remote powershell script should be doable.

For some perspective though, if you automate this as part of a CI builds it should be a once off cost, it's not a justification to make something a web app instead.

There are multiple solutions for handling updates of native apps.

Managing updates to a cluster of backend servers is at least as difficult, because they usually have shared state (a database).