The market is slowly waking up to the idea that in the future, conversion between altcoins (and bitcoin) will become nearly frictionless, removing any barrier for value to shift between altcoins. Due to open source, any improvement to the bitcoin software can instantly be adopted by the altcoins.
The market caps of alt-ledgers will ultimately reflect their utility - primarily their utility to Bitcoin, thanks to frictionless conversion.
There will be little if any utility in an endless supply of blockchains for merchant adoption (Bitcoin, Litecoin, or another will hit the sweet spot), so in terms of inflation issues we are talking about
store of value here. Why on earth would you store your value in any but the most scrutinized, monitored, long-running, stress-tested, brilliant dev-backed blockchain? I could see diversifying into a few alt-ledgers, but not more than a few, and only in proportion to their excellence in terms of dev team and track record. The rest would be speculation based on future promise, but that is even more limited. The marginal utility of each additional alt-ledger very quickly drops off.
All this amounts to very, very little inflation in the grand scheme of things. Even 200% total inflation would be negligible from a present-day perspective. Do you really care if 1 BTC ends up being worth $1,000,000 or $3,000,000? Even if LTC magically kept rising to equal the BTC market cap (which would be insane since it doesn't have nearly the dev support or track record), it would only slow down the average yearly tenfold growth of Bitcoin's price by 3-4 months.
Moreover, this could be a solution to bitcoin's deflation problem
Deflation is not a problem. At all. Endless inflation would be, but that can't happen for reasons explained above.
I do grant that if, say, LTC rises high enough it could create the
perception that altcoins could proliferate endlessly, and that could cause a short-term crash, but long-term not at all. People would soon figure out that it's all about where the development talent, the mining support, and the track record is. The first two gravitate toward the biggest or most useful ledger, and the final one is a permanent advantage Bitcoin has unless a catastrophe happens (and if it survives that, it's track record might be better than ever, with no other ledgers having weathered such a catastrophe).