I can't really comment on Guiding, but as a Beaver Leader there are a few points that may be worth making.
The Scout movement is equally oversubscribed - our own Group has a waiting list of 20, and all 100 places are filled.
Any Group that takes children's names from birth it nuts, IMO. By the time they are 5 or 6 half of them will have moved, not want to join Rainbows but want to join Beavers instead (or vice-versa). All they do by putting children down from birth is create fictitious waiting lists! We allow siblings to be put on our list from a sensible age ( 3 or 4 years old) and then everyone else can join the list from age 5. AT least by then you know if your DD is the type to actually enjoy Brownies!
An existing CRB check for a school is not valid for regular help at Guides/Scouts - you have to complete a new one for each organisation. (That will change soon with the introduction of a "portable CRB" - the ISA.) In Scouts the rule is that you do not currently need a CRB check if you help less frequently than once every 4 weeks and you will not have 1-2-1 contact with children or be staying overnight with the children.
Sadly one reason for the shortage of adult volunteers is that some Groups actively exclude parent helpers. I had to literally fight my way in to our Group 6 years ago, assisted by just one supportive Leader. That scenario means that, as parents never get to find out what is involved, they never sign up as Leaders.
Of course, the other thing is that some people are just too self-centered to give their time. One Mum recently refused to help on the rota because she said that the hour a week her daughter was at Beavers was "me time" for her.
She has one child and doesn't work ...
Gigantaur, I was never a Cub, Scout Guide or anything as a child. I pitched in and learned on the job. If you have the time to spare, please, please find a Scout Group or Guide Group and just ask to visit them for a couple of evenings to see what goes on.
We also make a point of offering places to the children of people who want to be Leaders. Some might disapprove, but if you are willing to volunteer I personally think you should get something back if possible. You don't have to do hours of training - there are simple "assistant" places that require very little training.
At the end of the evening I was chatting with a Dad and he said "I think that you do the most wonderful job", and his nearly-6-year-old son piped up quite spontaneously "So do I Red Beaver. You do a really, really, REALLY good job".
Moments like that make it all worth the effort.