What about a personal caching relay? Does that exist? So your personal relay is online anyway, cant it monitor your follow list and cache that, so when you open the client on your phone it just needs to fetch your relay. In this case your personal relay is actually acting as a client in a way. Sorry if Im asking stupid questions, been here for a good week, just trying to grasp this...
Discussion
I couldn't agree more with your idea. This is one of the reasons why I developed nostr-relay-tray and jumble. nostr-relay-tray can now enable non-developers to run a personal relay easily, and it can be accessed from the Internet without any configuration. The next version will support automatically pulling events from people you follow. Then nostr-relay-tray will become the personal caching relay you mentioned. And it can be browsed easily with jumble.