Battery weight, size, capacity, and charging time are all important attributes for electric cars in general. R&D is being done to address all of those things, with varying success. You are correct in noting that even if a battery is capable of recharging in minutes, delivering that much power safely in the real world has some major hurdles. Other replies have mentioned battery swapping as one workaround. Another workaround that I'm hopeful for is batteries full of electrically charged liquid slurry. You would pull into a "gas station", the slurry in your battery would be pumped out to be recharged on site, and a fresh load of charged slurry would go in.
Each potential customer has a threshold of what is good enough for their individual needs. I got a Nissan Leaf a year ago because my threshold is pretty low, and I've been extremely happy with it. On the rare occasion when I need to make a trip that exceeds my car's capabilities, I just switch cars with my wife. If I couldn't do that, my threshold would be higher.