I used to manage a volunteer co-op. Unfortunately just allowing anyone who wants to pitch in volunteer doesn't work well because if they don't have the skills to do the job (and that includes skills like basic organisation and initiative) then you simply end up spending more time managing them then they actually help you.
That said, I know it must be crushing to be rejected from a volunteer job so if we didn't think someone was suitable for the job they'd applied for we'd try and find something else they were good at. For instance, we had one old boy who just wanted to tidy the yard, flatten the boxes and have a chat and he happily pottered around doing that. Unfortunately big charities may not have that flexibility.
As others have said you don't need to apply to somewhere to volunteer. If I am cycling on tracks I normally head out with a bow saw and hedge trimmers in the bike (sometimes a lawnmower too) to cut back cycle path undergrowth. Very satisfying and, as others have said, if you wanted to volunteer along those lines take plenty of pictures and you can include them with your application.