Yes, banks do that. Many even prohibit employees to have personal brokerage accounts at other banks (How does that work for a married couple that work for diff

Yes, banks do that. Many even prohibit employees to have personal brokerage accounts at other banks (How does that work for a married couple that work for different banks? There are exceptions which require additional disclosures, like submitting you spouse's and/or minor child's monthly statements within some short time frame). Banks are the exception. Very, very few not-a-bank companies do that.