Yep, I train fasted on some days if I'm fasting for 24 hours. Like you've experienced it works just fine, you feel alert and focused.
Generally I have an afternoon eating window (2-7) so I do most of my work in the morning while fasted and like you I like the feeling of grabbing a hot drink and getting straight to it.
When I 24 hour fast I tend to fast between 7-7 and that's generally when I train fasted. I'm midway through a 24 hour fast today and will be training later right about when the 24 hours is up!