I have to study for certifications and generally expand my technical knowledge outside of work. It's not constant, but my quarterly objectives aren't achievable without "homework."
Everyone is different though. Some people have lower stress jobs where they work for a single company and have plenty of time to learn new stuff on the job (or never really need to acquire new skills). But I work in consulting, so acquiring new skills while maximizing my billable hours is part of the game.
I don't think its fair to call non-billable hours "homework". Having non-billable hours is part of running your own business. If you own your own business, you can do your nonbillable hours at any time in the day, including not in normal working hours, but you can also do your billable hours at any time of the day.
It's studying or writing (not billable work) that I must do to achieve a good "grade" (i.e., performance review) and it occurs between 9 and 11 pm -- long after I've left work for the day. That's the textbook definition of homework.
I'm also not the owner or anything of the sort; I'm a mid-level IC with no direct reports.
Everyone is different though. Some people have lower stress jobs where they work for a single company and have plenty of time to learn new stuff on the job (or never really need to acquire new skills). But I work in consulting, so acquiring new skills while maximizing my billable hours is part of the game.