Someone on our association committee recently suggested that we should consider going self-managed (we're a council site). He had done the maths for the rental income (I doubt he was anywhere near the right figure ...) and simply saw lots of ££££.
He got roundly shouted down! It takes a lot of time, effort, commitment and thick skins to self-manage. We didn't want that hassle. It's a totally different level of organisation, accounting etc etc.
All the points in Crowndale's post are really relevant. Sometimes there are unforeseen problems with a site e.g. drainage. How do you raise the cash for that? Perhaps also ongoing maintenance issues including grass cutting or tree surgery. We hire a tree surgeon once a year and it's well over £100 for the day.
I really can't see £10 p.a. raising anywhere near enough to have adequate reserves (at £10 you are paying way under the average). Our water rates alone are £5 p.a.
Consider how much it would cost to print your invoices, buy envelopes and post them out. And that's before reminder letters, warning letters etc. I doubt the parish would provide a post-devolvement subsidy for this - and even if they did to start with, they have limited funds and you can bet your bottom dollar that this type of funding may be a target if and when cuts need to be made.
Other things to consider include how you would resolve disagreements within the committee - whether personality clashes or differences of opinion re organic / warning letters policy / who gets kicked off etc etc. I think you'd also have to get public liability insurance cover for the site.
Grants for allotments are not as widespread as in the past - and they usually come with a community involvement requirement, not just to benefit existing plotholders.
Some self-managed sites thrive, don't get me wrong, it's the right course of action for some sites. But I think you are right to be concerned at what's behind the parish's suggestion.