Hi Jon,
php-xmlrpc extension is declared optional / recommended only (not required / mandatory). That means that you can run Moodle without xmlrpc perfectly.
You only will need it if trying to use some features:
- Mnet (inter-server communication and authentication plugin).
- xmlrpc web-services server.
- Mahara portfolio.
- Course publishing @ old moodle hub.
- ...
If some of those features are needed, right now, the only option is to install the beta releases @ PECL that you've commented above (https://pecl.php.net/package/xmlrpc).
Finally, note that there is MDL-70889 about to discuss and decide what to do with all that xmlrpc-dependent stuff because, clearly, the extension available @ PECL is not maintained, old and we need to find a replacement or remove / move all the features above to something better.
Ciao