wbknght +1 if its still possible to update one by one.
Sometimes its not a good idea to role out an update across your whole estate at the same time. Imagine there is an issue and ALL your servers are down now.
Maybe make the update all button stagger the updates with a customizable delay between successful update and the next server. A stop button to stop the update progression.
You could also write a ansible script or something similiar that deploys updates, check uptime of sites on that server, proceed.