I've tried it on my work computer a couple of times, but mostly I trade with my phone because it's more convenient and I can trade anywhere I'm as long as there's an internet connection. I don't think it's a terrible idea as long as the computer you're using is fully protected and the anti-virus has been updated and you're also making sure you log out whenever you don't use it, especially if the work computer is common to anyone at work to make sure that nobody can use your account.
The problem is can you focus on both tasks? Anyone can do both but not all, it's a terrible idea if you can't do your job properly because of trading.
Having a job gives you a stable income and if you lose that then it will also put your trading at risk because you have no source of funds.
Being well blanced types of person will give you this priveledge but like what you have said, it's not everyone who can deal with this and if you
failed to keep your time in the right way both sides of your sources of incomes will be ruined to the point that you'll be losing both.
Assess and keep being focus use your time in the right way and in the place and time.