Limited range cars with long recharge times would be a poor operating fit for economics that favor high utilization. There'd be too much downtime during peak times of day.
Maybe it could be coupled with swappable battery pack stations that the autotaxis could visit to get a freshly charged pack. A geographically focused taxi company could have the financial resources to invest in the battery depot, which would also solve the standardization problem.
Sorry, that's been solved. There are efforts to implementing this exact network of fuelling stations (battery swapping) for electric cars, and Better Place is a shining example from Isreal:
On the other hand, if you find yourself running low on juice, either because you're on a long trip or because you didn't plan ahead, it's not a problem. You just swap cars like the Pony Express swapped horses.
Lower utilization is balanced by lower energy costs than gasoline (but you're right, swappable batteries would help too).
Maybe it could be coupled with swappable battery pack stations that the autotaxis could visit to get a freshly charged pack. A geographically focused taxi company could have the financial resources to invest in the battery depot, which would also solve the standardization problem.