This is my first year in my current school so I can't remember the exact timetable and split between morning and afternoon groups, but after the first 2 weeks of term when older year groups are in and we have done home visits and most of the admin, the staggered starts only last 2 weeks, gradually going from 2 hours to including lunch, then adding another hour then a full day.
It's not going to suit every child but that's the nature of a school where there might be multiple classes of 30 in each year. Decisions won't always be made in the best interests of individual children. Sometimes you will have yo accept being inconvenienced because someone else with a different overview of the situation has a different opinion and a decision has to just be made for efficiency. Schools have to go on what works best for the whole community, so the other 59 Reception kids in my school, plus the way the school is laid out (eg can we bring the Reception children in, show them round , have an early lunch at odd times etc without disturbing the older ones) and the workload and working patterns of staff. That will be the same throughout the school years. It might not suit you and your child might be fine full time from day one, but having several children on different timetables within the same class would not work for the group as a whole.
In my last school, any reception children there all day during the staggered starts would be sent to play with year 1 and 2 while the Reception staff all had their lunch break. There wouldn't necessarily be lunchtime staff allocated specifically to Reception yet because we wouldn't be expecting anyone to stay, and it's not worth paying someone to just be in charge of a few all-dayers for an hour. The lunchtime staff there in KS1 have enough to do keeping the other children safe without spending extra time comforting the Reception kids as much as might be needed. Barring injury or tears, the kids would be left to get on with the older kids without support. Or just hold a lunchtime supervisor' s hand cos she wouldn't have capacity to sit down with that child etc when they already have a load of other kids to keep safe.
Basically, you could leave your child there all day but it wouldn't necessarily be the best thing to do even if nothing goes 'wrong.' Kid might be bored, not have / make friends etc. Would inconvenience staff which is not the best way to start that relationship.
If you genuinely want to change the staggered starts timetable, suggest a viable alternative such as a shorter period, working from a couple of hours to full time over a coffee weeks. Explain why this would be better for families and children. Complaining won't get you anywhere because schools know some parents will find staggered starts difficult. However, they also won't throw open the door to full time starts for everyone from day 1 because it is impractical and will be seen as not the best for the majority of children. Calmly and respectfully suggest an alternative and they might change it in the future. It would also be better for your relationship with the school should any problems come up in future. Complain that you don't want it for your child so the system is wrong and you will just annoy the people educating your child.