I would be really nice to have the church apps available on multiple platforms. Many years ago I worked on some commercial cross-platform apps. In one case, we had a common engine written in C that we could compile on Mac and Windows, but we implemented the GUI with native APIs on each platform. In another we used a C++ cross-platform library (we found a framework that actually handled platform differences quite well). I agree there are many tradeoffs. It's exciting to see several tools these days for cross-platform apps. One benefit I like for cross-platform is the reusable codebase. Depending on how the app works, you could have a substantial portion of stable, mostly bug-free code that's reusable across platforms. However, you'd still need to devote testing resources on each platform to make sure it's working properly...so even if the church leaders decided on a rewrite in one of these frameworks, they may decide they don't want to go to the expense of testing and publishing on all the platforms the frameworks can target.
russellhltn mentioned above about volunteer efforts to make things happen. Many years ago the church made a big effort to get volunteers to help with projects ("LDS Tech" was much more than a discussion board at that time), but apparently that didn't go as well as they had hoped, since all that seems to have been discontinued. So, I imagine it would take a lot of convincing for the decision makers to try embracing volunteer efforts again, even if it was just testing. There are archived beta test forums here on the discussion boards where they were trying to get helpful feedback from people testing, but they haven't used such forums in several years, so my guess is that didn't yield the desired results. With Apple making efforts to make iOS apps run on Macs and Microsoft making efforts to make Android apps run on Windows, maybe that's going to be the solution. mhenshaw's comment above indicates is working on a Mac.