I’m not sure I know the answer to that question. It’s definitely not a trivial problem to solve, but also not so crazy that it couldn’t be solved with some concerned effort. There are already some 3rd party services that will host your Mastodon for you, but as far as an easy to use mobile app, could be a good business opportunity for anyone with the right motivation.
The obvious answer there is "ActivityPub over SMTP". There is literally nothing that could go wrong![1]
(Basically a service which holds "ActivityPub postboxes" which collect events when you're offline and you pick them up in a batch when you're back online. The XMPP people already solved this one, IIRC.)
[1] Ok, there might be -some- problems.
Also, you'd need a backup server to render the "I am hiking or driving through a tunnel" error pages.
I always have the same concerns as you're pointing out, so I don't mean this critically, but reading your comments made me realize most of them could apply equally to either type of system.
Sure anyone can host a server but obviously that's pretty technical.
If you don't host your own server then you place a lot of trust on whoever owns it. They own your data and they decide which external servers to share data with. Want to add a video game centric mastodon server to your feed? Well you better hope your server decides to partner with that server.
Not to mention that servers cost money, so you have to be sure that whoever is hosting it can continue to pay for it. Mastodon the organization is a non profit. Do they have the funds to host millions of people? Probably not. Which means people have to find a smaller server and hope that it stays funded.
This makes choosing your mastodon server a pretty important choice. Most people seem to be going for mastodon official servers which is causing them to be overloaded.