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.
Yes, it is simply hard to focus on two tasks at a time. Most of the traders who go on trading at work weren't professional traders. Only the professional traders requires more time, as it is the primary earning for their living. When someone has got a work it'll be enough to meet the life needs. Trading is secondary source upon which less time or leisure time is enough.