I like the idea of getting rid of it in early education - mainly because, really, homework doesn't matter at all at that point since it's not really teaching anything and with the amount of help that most parents give their kids with it, it probably isn't worthwhile. Later on, though, when the parents will be helping less and the education actually matters, hell no do not ban homework. If it'll help kids learn then by all means, use it.
Really the workload both in and out of school below a more advanced level i.e. these "AP Classes" which I always hear you Americans talking about or actual university degrees isn't nearly as bad as people make it out to be and an hour or two of solid concentration per day outside of lesson times can easily consolidate what you learned earlier that day. If, with the relatively short school hours that most (note: most) kids have, they still find themselves unable to dedicate a simple hour or two to their work then they're either prioritising their use of time wrongly or are just plain lazy, unless there are exceptional circumstances like being a child carer or something like that, but that's a whooooooole different case which needs approaching differently. As for the earlier mentioned higher-level stuff, if you're studying a subject at a higher level and you're complaining about the workload to the point where you want homework which you know will help you banned, then it's really time to reconsider whether or not you actually should be doing that subject.
Regarding longer school hours in favour of banning homework - no. I don't think the quality vs quantity argument here is really relevant since homework and lessons are intended for completely different purposes; lessons are to teach new information, homework is to consolidate existing information. If homework was there to teach you something new (which, on rare occasion, I suppose it is) then fine. Maybe extra lessons would be an option. But there's no real point that I can see of replacing something with something else made to fit a totally different purpose.
Bottom line is that I don't think homework is as big an issue as it's made out to be and I definitely don't think there's any good reason to ban it. However, I get that some kids just won't do it anyway. I was definitely one of those kids for a loooooong time lol, although not really any more. So I feel like if homework's not done then it should be at the kid's own choice. If they want to harm their education, let them. By all means encourage homework but remove forms of punishment, failing (although in England you'll never fail a course because you didn't do its homework and I think it's ridiculous that any education system can allow that to happen), etc., from students not doing homework. It essentially becomes optional. I know that it's likely that the majority of students won't do optional homework, but really, is that a bad thing? It sets the students who really want to work and really want to get somewhere in later education apart from those who don't. I don't see a problem there given that it's the purpose that lower education systems are made for.
tl;dr don't ban homework because it's unnecessary to do that. Make it optional but encouraged instead.
disclaimer: I am talking with regards to the education system which I know here. Maybe something here wouldn't fit well into an American system or otherwise, idk.