Go ahead and be that parent if you work and they have a school place. They are legally entitled to a full time school place from Day 1. Old, but I have this my documents from posts on here previously that I sent to some friends:
"It is illegal for a school to insist on a staggered start. Any parent who requests a full time place from the 1st day of term must be given one. The office of the schools adjudicator has ruled on it many times and has included it in the annual summary
If you want full time from day 1 and you are in England then tell the head that is what you want. If they refuse then direct them towards the office of the schools adjudicator ruling that I linked to earlier.
If they still refuse. Contact the LA admissions if they are the admissions authority. If they are not the admissions authority and it is an academy then contact the EFA.
If needed follow up with a formal complaint to school with threat of school adjudicator (but it won't get that far)
The school don't have the option not to be accommodating. The law says that if a parent requests a full-time start, they should get it. The school wouldn't be doing the OP a favour, they'd be doing what they are mandated to do by law.
...............
webarchive.nationalarchives.gov.uk/20160808140848/www.gov.uk/government/uploads/system/uploads/attachment_data/file/484942/Office-of-the-Schools-Adjudicator-annual-report-September-2014-to-August-2015.pdf
2015 support paragraph 62
The Code at paragraph 2.16 requires schools to make provision to admit children full-time from 1 September after their fourth birthday. Those children born between 1 September and 31 December reach compulsory school age of 5 years old at the beginning of the term after 1 January and for those born between 1 January and 31 March this is the beginning of the term after 1 April. Until a child reaches compulsory school age parents may choose to delay the admission of their child and/or their child can attend part-time. Paragraph 2.16 makes clear that it is for the parents to decide whether their child attends school prior to reaching compulsory school age and if so, whether attendance is full or part-time. Schools must make full-time provision available from the beginning of the autumn term of the school year in which the child reaches compulsory school age, the September following the child’s fourth birthday. The OSA has again had queries from parents about their child’s right to a full-time place. Some schools provide an induction period such that it appears schools dictate the sessions for which children can and cannot attend school, including setting requirements that contravene a parent’s right to full or part-time or deferred schooling contrary to the requirements of the Code.