Sure, but lead-acid and zinc-carbon, both 19th century technologies, were the main - essentially only - types of batteries until the age of the Walkman in the 80s. Then we got Duracell alkalines and cute adverts. Until then there wasn't a lot of pressure to get better, so they mostly didn't and they wouldn't have sold anyway. Around the same time rechargeables got some development pressure in the form of mobile phones, and there was effort to do better than rubbish NiCds or heavy lead-acid. Even cell sizes remained constant for nearly a century. If there'd been more pressure there'd have been a lot more chemists thinking about improvements than just Ever-Ready, Duracell and Motorola.
Maybe a global electric car industry working on the problem 4x longer than we have would have come up with something better, maybe not. Alternate time lines are never certain. :)
Batteries aren't all of it though - how would personal transportation have evolved if every city and road network had electric distribution points for vehicles - as was planned in the 1910s - instead of filling out with petrol stations? The fast charger networks could easily have been something of the 1940s rather than the 2000's. We'd undoubtedly have standardised on a generic one that worked with every make of car by now. We'd probably have designed cities a little differently too.
Be careful: For the improvements, are close against some quite fundamental chemistry and physics. E.g., for fast charging, the battery has internal resistance, that is, gets hot when charging. Likely the amount of internal resistance varies, but charging as fast as filling a 20 gallon tank of gasoline might encounter something impossible due to the chemistry/physics. Fast charging is one of the reasons for the pursuit of capacitors instead of batteries, e.g., the EEStore effort with barium and titanium. The capacitors also typically are able to discharge much faster than batteries. IIRC, battery charging is a chemical reaction where have to move atoms around. A capacitor, first cut, just moves electrons around. But for research time, EEStore has been at it for some years now.
Maybe a global electric car industry working on the problem 4x longer than we have would have come up with something better, maybe not. Alternate time lines are never certain. :)
Batteries aren't all of it though - how would personal transportation have evolved if every city and road network had electric distribution points for vehicles - as was planned in the 1910s - instead of filling out with petrol stations? The fast charger networks could easily have been something of the 1940s rather than the 2000's. We'd undoubtedly have standardised on a generic one that worked with every make of car by now. We'd probably have designed cities a little differently too.