Ask HN: Are small blockchains secure?

I finally read the Bitcoin white paper and there's one thing I don't get. The security relies on the majority of miners agreeing on the state of the global ledger, where "the majority" is measured in computing power.

It seems reasonable to assume that the computing power of a malicious miner doesn't stand a chance against the enormous hashing power currently devoted to Bitcoin, but what about smaller blockchains? Couldn't the biggest Bitcoin miner just switch all their resources to Litecoin for a few minutes and cause complete havoc? I imagine the smallest blockchains could be hacked/ruined just by someone with a fairly high AWS Lambda rate limit.

I keep hearing about new projects to use blockchains for every little thing, and I just can't imagine how any blockchain other than the big one can be secure.