Airlines care a lot more about weight than you do. If they rented out batteries I expect they'd go for lithium or NiMH because of that. It'd be interesting to see how the economics actually worked out.

There's also the question of giving someone 5kg of dense, caustic material with easily accessible energy (even an SLA will give you a decent spark or red hot wire). The anti-tourist people would probably veto it just on those grounds (but still let you take your laptop battery).