Many people do but maybe they shouldn't? If there is a firewall or something like that in place to stop you (general you) accessing a private account, then doesn't that say "you're at work and shouldn't be doing personal business on company time"?
That is an extremely unrealistic statement. Some personal business can only
be conducted during 9-5 business hours. The firewalls are not to restrict you from doing personal business from your office, they are generally set up at institutions as a security measure to protect sensitive data.
For example, my friend works in finance. All external email programs and social media platforms are blocked because they must
be able to track and log communications leaving their business. It protects the company from things like allegations of insider trading and helps to mitigate other security risks, such as sending very sensitive information over unsecured networks or easily hackable systems. For example, my Yahoo email was compromised by the Heartbleed bug, I can guarantee my friend's workplace servers were not. His computer also doesn't come with any USB ports or anything that would allow portable data storage, so he could not take copies of sensitive data out of the office.
My SO can only use office email while at work. Luckily, we've never had a service provider do something silly like copy information from a signature and use that to update their records without permission. That's very
unprofessional of them.