Only thing I can think of is to mod more memory to the phone. Local storage on mobile is a laughable concept, they're not full-blown computers and most of them aren't even "smart".
(This is purely an opinion but I'm very much willing to take any and all the reputation hit for it.)
Late edit: A bit further clarification, consider iPhone: Its browser allows the user to open up to 8 tabs at any time. It's first models has 128MB of RAM and newer models have 256MB of RAM. Now, allowing 5 megabytes per tab and 8 tabs mean that just the cached content may take up to 40 megabytes of those precious bits which is already quite a lot since I really doubt that the browser itself, not to mention phone's OS and other stuff hanging in memory wouldn't take a significant part of the memory already.
On top of that as long as even a single old-generation iPhone exists, Apple has to support it on software - it wouldn't be good for the image of the company (not that it'd be that great at all anyway currently) if some of their everyday products would just stop working all the sudden.
In short, it's just not feasible to allow local storage to expand beyond a few megabytes because phones just aren't capable to do that. Wait a couple of years and then maybe...