What are the space concerns for keeping data in this way? For something like a retail bank (audit issues aside which probably make this necessary anyway) does space suddenly become a big factor?
Double-entry book-keeping is done this way. The data certainly grows over time, but generally at a predictable and manageable rate.
Most people using long-lived event-sourced data structures have some kind of snapshot/checkpoint/archive mechanism, which going back to the accounting example might simply be an opening balance.
I think the more realistic concern with this approach is that some queries might get complicated when they involve more complex logic based on the balance.
Solved or made worse by caching?
Caching may relieve some stress (on say a dashboard), but if an application is doing calculations around account balances, and uses event sourcing-like structures in the database, then caching isn't going to help as those calculations are going to still need to be done for each new balance changing event.
So caching is never worse (unless you accidentally used the cached value where you needed the live value), but isn't necessarily going to relieve a lot of DB stress.