I would rather have the Fed purchase corporate bonds sold by the companies. That way, the Fed wouldn't control private industries or elect company board members, it would simply be a creditor. Yet the companies would still get the $ they need to survive. Commercial paper effectively does this (but on a short term basis).For the record, I'm making a prediction. The Federal Reserve will purchase stocks outright if the stock market doesn't respond to stimulus ($1,000 checks to adults, suspension of payroll taxes etc.). If Congress is slow to enact these measures or if the markets accelerate downward before they can be enacted, the Fed will move ahead with stock purchases regardless of its mandate or legality.
A problem is extending the commercial paper to, or having the Fed purchase bonds from, smaller and smaller businesses, who arguably need it the most.
Of course, there is precedent for the federal government buying equity of a private industry, then selling it off after the crisis--GM.