I think it will vary frankly, while the patrol vehicles use diesel still they can easily provide some electrical current, from the engine plus a relatively small battery built into the van.
Even when towing it takes them some time, they have to get out and setup the tow hitch, so if its a choice of charging 15 miles worth at the roadside or towing 5-10 miles then its probably quicker and safer in many cases to just charge there.
Flatbeds can take hours to turn up and cost a lot more.
They will normally spend up to an hour at the roadside I believe, so its hardly a stretch to give some juice.
Hell they may even create a better van, so one thats purely for EV running out of juice. The issues faced and fixable at the roadside for Evs vs ICE cars will be dramatically lower.
So imagine something like the tesla truck arriving with a socket to plug into. A real time map of nearest charging points (hopefully far smarter by then, maybe even allowing a pre booked slot, book and pay in advance) and its far more feasible that roadside mini charging will be a thing.
Or if it really becomes an issue then a port to allow a decent size lead acid or similar to be dropped in that would provide a bit of charge to do say 15 miles. AA drops the battery in, follows you to a charge point, takes out battery sticks it back in his van and drives off. EV driver watches netflix for an hour whilst he charges.
So many options on how this could work I really dont see it being a terrible problem in the future. I still think it will be over hyped, as the charging expands and it becomes the norm for people.
Hell people in hire cars are probably a good example of a worst case example, they frequently also do idiotic things like putting the wrong fuel in. Its why they pretty much always have a sticker on the cap saying which fuel to put in.