In a normal financial crisis the government tries to maintain the stock market prices to prevent a spike in unemployment as companies collapse and run layoffs. But given that we're in the midst on a pandemic with 30% unemployment, what are the benefits of propping up the stock market rather than letting it crash to 2009 levels?
The government(s) [probably] assume that this is lockdown is a temporary situation so having companies fail during the lockdown would mean that when the lockdown is lifted there would be no jobs for the unemployed to return to. It's true that in completely laissez faire approach you could also assume that the companies would be recreated quickly, so everything would return back to normal on its own, i.e. just by market forces, once the lockdown is lifted. I think most governments don't think like that though, i.e. they can "foresee the pitchforks" if after the lockdown is lifted, the unemployed find no jobs then (quickly).
Basically, your assumptions are inconsistent: on one hand you assume that the gov't should smooth out the "business cycles" in a "normal financial crisis" (whatever that means, I guess you mean recession--financial crisis are generally atypical as far recessions go and there's more than one type of "financial crisis"), but on the other you say that they shouldn't do this now because the recession is caused by the pandemic lockdowns. If anything, the latter is an even more obvious case that a "business cycle" is happening.
Also, I think it's usually not a direct objective of the government to "maintain the stock market prices", it just happens as a result of their desire to stabilize the "mainstreet economy". (Trumpian rhetoric equating one with the other aside.)