Merf, you misunderstand. The discussion is not about the maintenance of communal areas on a site, but the use of borrowed or hired mowers / strimmers etc. on a plot.
The use of one's personal mower at home on one's personal lawn is not at all comparable to the situation where an entity owns mowers and lets people borrow or hire them for use on an allotment. At home, you know who has used the equipment, know how it has been maintained, take everything at your own risk, and nobody else is involved.
Where you borrow or hire a piece of equipment, you are legally entitled (and have been so entitled for decades) to assume that it is maintained / serviced properly, and safe at the point of use, for starters. If you are injured using it then you can sue the entity for damages. Think of McDonalds being sued by someone who got burnt by a cup of hot tea. Insurance is a must - as a general rule, most allotment associations are unincorporated associations and therefore all the members are potentially liable for the damages if not insured.