I suspect the Charities Commission wants organisations to apply to be CIOs using one of their two (long) model constitutions for two reasons:
1. If you submit their document, edited so that they can see clearly what you have changed, it is much quicker for them to decide whether they like what you've added or changed or not (they know they like what you haven't changed because they wrote it!). So, printing their document and making the changes additions using a pen, makes life easier for them.
2. There is a lot of detail in their documents and becoming a CIO is a serious, legal thing. So, having the initial trustees sign to say they agree to all 26 pages, is appropriate if you look at it from their point of view.
That said, I know a number of Sheds that have started from another Shed's successful CIO application and that seems to me to be the way to go - you still have to read and sign it, but there's less to re-invent (such as the objects, which have to meet certain criteria).
I can't speak for Havant but it seems to me that the simple, short constitution (which is really clear and simple) at:
http://www.havantshed.org.uk/CONSTITUTION.pdf is not what was submitted to the charities commission; the submitted version is at
http://www.havantshed.org.uk/CIOConstitution.pdf and looks like it is one of the CC's model constitutions duly completed and edited. It got them CIO status in Aug-2016.
The message seems simple: If you want CIO status, accept there's some work to do and use other Shed's successful applications as a model for yours. We're nearly there at Basingstoke having been guided by Reading's successful application. The only bits that got rejected by the Commission were the bits we changed!