It's "homework" in the sense that it is not bound to the class. It is not due during class and if you can't finish it in class, you'll have to complete it out of class.
And I mean setting aside some time during the class itself, not a separate "study hall" period. Obviously class time is precious, so I don't expect there to always be enough in-class time to finish assignments. But even having a little in-class time for students to get started - and when the teacher is available for help those in need - would go a long way towards encouraging students to do the work themselves and not cheat.
And of course part of my strategy is to make "homework" shorter (5-15 min). That should also reduce the temptation to cheat and increase the likelihood students can even complete them in class.
Assignments students do in class isn't "homework". It's just classwork. All my math classes had both.
Perhaps you mean study halls? Those were uncommon until highschool where I grew up. And most of the time people spent there was not studying.