For what problems would be solved; I believe the main hiccup using Bitcoin is scalability and volatility. Volatilois not much of an issue as it gives it speculative value, and I personally do not see it reducing in the future (in relation to fiat), we could at a time be seeing $5k candles +/- when Bitcoin hits a far higher price. There are lots of proposals to fix the scalability issue, so I'll expect something to change with the next five years.
For what problems would arise; my major concern in privacy issues. Centralized exchanges are getting more popular and this could pose a major privacy problem as governments seeks for ways to control the network.

Off chain txs cannot replace on chain ones as it has to interact with the network at some point. Although, I expect LN to get more popular.