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You can look at the block rewards and mining fees as interest on your investment. The "saved" part is interesting too - I've seen variations where you have to lock your stake for a longer period (trading rewards for liquidity) or where you have to "burn" an amount of stake, permanently taking it out of circulation to get a spot on the line.

The inflation rate and actual utility of the currency are important factors too - if most of the currency is already distributed and the inflation is low (thus block rewards are low), the richer don't get much richer. If the utility is high, redistribution occurs more naturally as well.

Perhaps the inflation is not low but there are other distribution mechanisms that distribute currency based on utility in a higher rate than block rewards (for example on steem, of all newly minted coins in a block ~5% goes to the block creator, ~65% goes to content creators, ~6% to commenters, ~17% to curators and 7% as interest to those that have commited their stake in a long term deposit).

But yeah, in the end it indeed is a factor which is one of trade offs I mentioned, but there are ways to combat it.