It's a horizontal inflation that is happening. I think in the long-run it could destroy the value storage function of crypto currencies as long as a fork brings a marginal profit for those who do it.
All these (seemingly!) successful Bitcoin spin-offs show that there is still a lot to gain from forks until the costs to pull off a fork (advertising, managing and mining) becomes more expensive than the selling price. 300$ for a bunch of useless digits is still way to go until it stops.
Looking at it from a strictly economic perspective, it will only stop when new forks have an initial value of zero and that means that Bitcoin itself will have a value of close to zero too because the cryptos may share the same market, but the Bitcoin versions share the same customers.