Stock returns and fund returns are on average not autocorrelated and thus unpredictable. Consequently, looking at a historical price chart gives no indication in which direction tomorrows price will move. Howevery, looking at price paths, investors can be fooled to see trends or patterns through framing effects. Thus, I wonder, what the use is of showing investors price charts?
Because consistency in returns can be a measure of fund manager's skill, the guy who'll manage your hard earned savings. That is why you should check something called "hit rates", which is the probability of outperforming benchmark. It is should be significantly greater than 50%, showing manager's skill and consistency.
Under Efficient Market Hypothesis, future prices are nothing but the expected value of historical prices, given a probability and an information structure.
Looking at historical prices can be useful. Indeed, a lot of the financial literature, spanning from Risk Management to Portfolio Management uses historical values.
As you suggest, however, in case of structural breaks/jumps in time series historical values are useless. Nevertheless, current market micro-structure is led by arbitrage pricing theories and a continuous of traded prices for liquid securities.
Thus, structural breaks are not that common, which makes historical values useful especially when used to gauge future values.
I hope this answer helps as I tried to talk about the philosophy behind using historical data - as in your question - rather than the assumed mathematical substratum.