If my wallet doesn't support RBF, there will be no option for me in software to increase the transaction fee. What's the point there?
The point there is to use a better wallet. 
Network rules are not bound or limited by third party developers failing to implement basic functions in their software. Being able to replace an unconfirmed transaction is an increasingly basic function of bitcoin. If your wallet does not allow you to do that, then find a better wallet which does.That sounds very logical! But kinda confusing for the nodes, wonder if it causes some kind of danger on network, something similar to double-spending.
The only danger is if you accept zero confirmation transactions. However, these have never really been safe to accept in the first place, but some businesses accepted that risk for the convenience they brought. Full RBF makes no difference to confirmed transactions.