First, Bernie said the concentration of political and economic power threatens democracy, not that there's a danger of default. It's just standard tactic of just throw big names in and mention " threats to democracy" and people start clutching pearls without understanding the issue. The irony is that the one he listed that really throws its weight around is blackrock, and they use it to force public companies to adopt DEI policies.
Second, comparing bank assets and fdic insurance to the securities industry doesn't fit because they're entirely different businesses and regulatory regimes. A bank's very business model requires it to loan customer deposits, and your deposit is really an IOU from the bank. If the shit hits the fan on the bank's balance sheet, well customers are fucked, absent fdic coverage.
In contrast, the various laws governing brokers (1934 exchange act and rule 15c3-3), investment advisors (1940 advisers act and rule 206(4)-2), and mutual funds (1940 investment company act and rule 17f-1 et seq), require each to keep non-margined securities separate and distinct from company assets. So if these companies fail, creditors have no claim to customer assets.