I so know what you mean. The purist in me would like to be up front about these things so that you are not feeling like you are misselling, but the reality is that I just don't think you will get a foot in the door of many roles if you are.
I can't think of many roles that go to agencies or headhunters as part time or flexible up front and this means line managers have in thier mind that they want someone who is full time doing certain hours.
Having said that you are not asking for a huge amount! Just to shift your working hours to do a pick up. If you were the candidate I wanted then I would be fine with this at second interview, or to be honest first interview.
I agree that if a company has said no to this then they are not very creative, forward thinking or flexible unless the role absolutely requires someone to be at thier desk until 5pm.
I wonder if it is how you approach it. If you provide the impression that you are fixed on 8-4 with no flex then I would be worried. I'd expect someone to manage their own work and deliver it whatever hours they were in the office.
If the individual wanted to do this and pick up kids, then no issue.
I also have a bit of a fate approach to this. If you stay true to yourself and do what feels right you will find a role you want and an employer that suits you. It just may take a bit longer than someone who just does the bog standard.
What type of role are we talking?