Is there a benefit in spreading funds across multiple separate accounts/brokerages? [the US]

This is not a question about different account types (Roth IRA, IRA, 401k ,etc.) I am just wondering if there is a benefit in opening multiple individual (non-retirement) brokerage accounts after a certain amount of funds. For example, when it comes to saving accounts, since FDIC insurance is limited to $250k per account, I believe it makes sense in opening a new account when you hit the limit.

What about brokerage accounts? I guess I am thinking about it from a systemic risk standpoint. Is it better to open a new account in a different brokerage after you have, for example, $250k in one account? Does it even make sense to be opening a new account in the same brokerage? Are there any protections similar to the FDIC that are limited per account?

I understand that there is more hassle in managing multiple individual brokerage accounts, like taxes and such. But are there benefits that outweigh those?