Lack of mechanical know-how seems to be more problematic en velo than en voiture, possibly due to lower likelihood of knowledgeable passerby (not to be confused with passing axe murderer & friends) and lack of AA/RAC cycling version. (Mayhap AA/RAC should extend the cover to cycled journeys "you're the member not the vehicle ...?")
I dunno. If we assume the average cycle journey is less than 5km, then it's not really that a big deal. Push it home; phone a friend; lock the bike up; get a taxi; take the Brommie on the bus; invoke the local
Bike Man Dan or whatever are all reasonable strategies, especially if combined with a bike that's configured for reliability (Marathon Plus, hub gears, that sort of thing).
I accept that I don't really have first hand experience of this one - though it is something I've worked through strategies for with people I've encouraged to cycle. I'm a competent enough fettler that all but the most catastrophic mechanical problems don't really scare me, and I've always reckoned that I'm probably one of the axe murderers
[1]. It's body failure that I worry about more (particularly if I'm a long way from civilisation).
There are bike rescue services. Maybe, along with mobile bike mechanics, they're worth making a bit more noise about to newbie cyclists?
Like 'hills' and 'weather' I'm not convinced it's as much of a barrier to transport cycling as it is a convenient excuse for car use. It may be more of a barrier to sport/leisure cycling.
[1] More seriously, I consider cycling to be a net personal safety win. I'd rather cycle through a nonspecifically dodgy area than hang around a bus station.