I would prefer the weekly/5 day turnaround system. As a working lone parent with 3dc there is no way we could do daily turnaround and dinner and clubs and baths etc.
Another example similar to chrisdrivers happened in my dd's class this yr. (Year 4)
A sheet with 6 different tasks was given at the start of the half term, all based on that half terms theme. It was up to each child which task they handed in each week, but one had to be handed in each week.
Some of them dd could see would need more time, and she learned about planning ahead and doing a little of the more time consuming tasks each week while also doing another to hand in that week iyswim.
I know another child who did the big ones firstas she had a busy time ahead with performances/grandparents visiting, etc.
Another child who couldn't attend school due to a contagious illness but who wasn't actually 'out of action poorly' got all his done in the week he was off. So effectively he had no homework for 5weeks.
Importantly these tassels taught so much more than the subject. And far more than a sheet of sums/grammar sentences etc. Each one required research, planning, and thinking about what resources to use. it made the child use literacy and mathematical skills, science, it, history and geography. (And probably many more that i as a parent and not a teacher am not aware of.) My dd realised she had skills she didn't give herself credit for. And despite her/our initial 'oh no' reaction due to something different, it renewed her interest in completing her homework and made her feel proud of what she achieved during that term.
I would be delighted to see a similar homework system again.