1) it’s not your ‘understanding’, it’s your ‘interpretation’ and it makes complete sense to think like that because you have no first hand experience. But you’re wrong.
Right, but a paramedic was the one who said to me that they can be helpful...so, no, not my interpretation. Perhaps the paramedic I spoke to was mistaken, but I didn't pull this out of my arse 
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2) Paramedics do a full 350 search regardless. The BOB sign is not comparable to a list at all because people have them in their cars whether their child is there or not. And people have children in cars without the signs. Paramedics don’t use a car sticker as an attendance list.
But, parents might take them down, which would be the best thing, if they choose to put one up at all. And even for those who don't, there may be a good chance their dc is with them in the car if and when they have an accident.
I didn't say it was exactly the same as an attendance list, but just something that people may use in the same way, to indicate there is a baby in the car.
Even though paramedics do a full check of the car, if they see the sign first, it might help them be better prepared, in a small number of cases.
3) I agree with you that there’s no need for the hatred of them and if it makes people feel better to have them then they should just crack on.
Good good! I'm sure people will crack on anyway and your blood pressure will thank you if you don't get yourself worked up into a rage every time you see one!