I wouldn't personally run something like this, but I've definitely experienced the frustration of having a user install an extension that changed my website, and then reported a bug in the extension to me.

Even when the extension is bug-free, it still adds a support burden. For instance, there's an extension that adds icons to usernames on my site. Users have asked me how to change their icon, and then gotten mad at me when I say I don't know.

It also adds a maintenance burden: Whenever I deploy various updates, I get complaints that the updates break one extension or another.

Not to mention, there are extensions not intentionally installed by users. For a while, there was some very common malware that rendered my website unusable. It added the text

    <script src="http://example.com/malware.js"></script>

    <script src="/legitimatescript.js"></script>

    <script src="/legitimates<script src="http://example.com/malware.js"></script>cript.js"></script>