I suspect free entitlement = funded hours for 3/4 year olds (which incidentally big disadvantage for some providers because they can't offer it).
And at the risk of derailing the thread again yes, nannies do things CMs don't do. Some CMs do things others won't. Parents sometimes don't want to use a particular form of childcare. It's an argument for demand side funding because putting money with the parents increases parental choice!
Consideration of all the different forms of childcare and how different funding types affect them is important. There are various forms of tax relief some of which would mean a sweeping reform of the current system and others which require subtle tweaks.
Deducting a larger amount at source is a simple administrative change. Allowing SE people to buy vouchers before submitting their tax return could work.
Supply side funding freezes out any childcare which isn't a CM or nursery/preschool and makes ad hoc arrangements difficult.
Making childcare wholly tax deductible where for example you pay up front and then get a reduced tax bill the following year would be very complicated.
So on balance strix has the best all round solution even if it's less advantageous for certain types of provider.