> I presume the rationale to increase the rates is that during the next crash there will be something to lower.
The rationale for increasing rates is to forestall inflation rising above the targeted level; inflation remains below targets and is expected to in the short term, so there is no reason to raise rates.
> What will they do if the market crashes and the rate is still 0?
Whatever they do won't matter much, just as it wouldn't if the market crashed with the rate target raised to 1/4 - 1/2 percent instead of 0 - 1/4 percent where it is now.
If the economy hasn't had the kind of strong, broad recovery that would support higher interest rates before the next crash, monetary policy isn't going to do much to deal with the next crash (and monetary policy isn't going to produce that kind of strong, broad recovery, either.)
The Fed as an independent central bank, while it has important responsibility, has a fairly limited role; most of the strong economic policy levers are fiscal policy that is in the hands of the political branches of government, particular Congress.