A few lines from the Blackrock CEO's annual letter(March 15, 2023):
"Over the longer term, today's banking crisis will place greater importance on the role of capital markets. As banks potentially become more constrained in their lending, or as their clients awaken to these asset-liability mismatches, I anticipate they will likely turn in greater numbers to the capital markets for financing. And I imagine many corporate treasurers are thinking today about having their bank deposits swept nightly to reduce even overnight counterparty risk."

"Governments are playing a bigger role in where products can be sourced and where capital should be allocated as they look to keep the production of critical components inside their borders. This means capital won't necessarily be allocated to the businesses that deliver the maximum market return regardless of where they are located. This may produce better national security outcomes with more resilient and secure supply chains. But in the near term, the effects are highly inflationary. This tradeoff between price and security is one of the reasons I believe inflation will persist and be more difficult for central bankers to tame over the long term. As a result, I believe inflation is more likely to stay closer to 3.5% or 4% in the next few years."
blackrock.com - Larry fink annual chairmans letter

My take on this:
Banks might look to the stock market for financing, but the sudden bankruptcies and decreasing earnings will not inspire buyers. Maybe those who are capable of navigating the heightened risks could use this as a buying opportunity.

The use of cash sweep accounts may increase, but there was confusion among SVB customers who used them. Some SVB accounts owned Blackrock money market funds, but the account owners could not access the funds on Friday during the bank shutdown. Blackrock told them the funds were in the bank's name. SVB was acting as a brokerage.

links
svb.com - Svb cash sweep
news.yahoo.com - Startups parking svb cash treasuries
bloomberg.com - Svb clients in limbo after seeking refuge in money market funds