I'd prefer that Chrome write "insecure" if there's a non-public CA in your chain.
1) Every employee of every company needs to have some level of trust in their company. They trust their company to make payroll, and they trust their company at a reasonably high level to follow local laws and regulations, including reporting threats and violations against their physical safety. That doesn't mean that employees should trust their employers with their deepest darkest secrets and life savings, or that there aren't different types of trust, just that trust is a spectrum, and arguing that you should fully trust every one of the shadowy public CAs pre-installed in your OS and browser, that you know absolutely nothing about and have not personally vetted nor have personal relationships with, but not the intranet CA your employer operates, is rather clearly an irrational assertion.
2) If you decide not to trust your employer's CA, and your employer has provided you with a machine to access intranet sites, then you clearly cannot trust accessing Internet sites for personal reasons on your employer-provided device, not because the CA cannot be trusted but because it's irrational to distrust the CA but also trust the employer-provided device, which may have a keylogger and other tracking software installed.
3) If you decide not to trust your employer's CA and your employer operates a BYOD environment, then you are free to bring a separate device for work purposes, on which you trust your employer's CA but refrain from accessing personal accounts, instead only accessing personal accounts on devices which your employer doesn't know about.
If it's BYOD, then create a new user account / profile for work. We're not running DOS anymore.
HPKP does not validate pins if they resolve to a user-installed trust anchor like an intranet CA. The RFC [1] leaves behavior undefined (see Section 2.4), and I'm not aware of any popular implementation that would honor the pin in case of a user-installed certificate.
This can be incredibly frustrating if you're trying to protect against MITM attacks; but at the same time, I can follow the browser developers' line of thought that goes "if we were to enforce it, users would just jump ship to the next available browser".
Commonly I only allow internal CAs for specific internal websites and not allow them to MITM just any website. On occasion this meant not being able to use the company's wifi and deal with 4g instead.
Certificate errors on "internal" web apps are just as bad as on the rest of the internet.
If I have to I trust the company's CA in a special browser profile that I only use for working with their internal tools.
For just a few tools it's often simpler to just trust those specific certificates, though