I completely agree about the interconnectedness of different branches of mathematics and think it is difficult to visualize and intuit because we don't yet have the language.

My guess: Eventually, as we begin to understand mathematics better, we will elucidate the underlying properties of theorems and there will be better "tagging"; the underlying language must also change. This will not happen for a minimum of 30+ years as new advances must be made and institutional faculty will object lest their life be rendered irrelevant.