They claim it's specific to the car I think.
Batteries for modern cars with stop-start, are a bit messier to change. Not exactly car-specific, but certain cars will need certain types of battery. It's not as simple as it used to be, when any old lead acid battery of the correct (or larger) capacity could be used.
"Precision" balancing is a thing. The wheel and tyre together, are a large rotating mass. They're also a 3-D rotating mass, in that it's more of a 'cylinder' than a 'disc' that you are trying to balance - which is why those DIY wheel balancers where you just balance the wheel and tyre on a sharp point and add weights until the thing sits level, don't work).
Balancing until the average driver can't feel any vibration is "good enough". However, it is always possible to balance something more precisely. If you've got an old van that isn't very fast, doesn't have ridiculously wide tyres, and is pretty rattly and wobbly, You're unlikely to notice something out of balance by as much as (say) 10 grammes. If you have a light, fast sportscar, you might be able to feel a wheel out of balance by 5 grammes or even less, if the road is smooth enough. So for your extra £3, they just take a bit more care (I imagine) and get it down to a smaller imbalance.
As others have said, it is complete hogwash that you need to rebalance each time you take a wheel off and put it on again (well, assuming you remember to fit it shiny-side-out"...
). I have two sets of rims for summer and winter tyres, so our car has all its wheels off and on again, at least twice a year, plus servicing. Never had a problem with needing to re-balance them. Likewise, suspension alignment.