Absolutely, no one who cares about privacy should be using their work phone as their personal device. You should always have two phones at least, one for work and one for personal. Work having access to your texts shouldn't be something you weren't already suspecting they had access to (there's other ways for them to have access to it). I don't even hook up my personal device to my work's wifi. I just assume all my work devices and connections have keyloggers for everything.

If you're on a personal device and care about privacy you should be using Session for messaging people. Signal is compromised.