The real question is, will it be cheaper than the gasoline you'd otherwise use?
The answer is - resoundingly - YES.
Your savings will be greater yet if you get a time-of-day meter, and charge at night when the rates are much, much lower because so much generating capacity is surplus.
You are misinformed about battery replacements being every 4-6 years. Coincidentally, that is the very frequency that most people have to replace their present car's starting battery. That is a cheaply made lead-acid battery. Compared to all the others, lead-acid is a terrible battery technology. It only excels at one thing: the huge burst of current required to start an automobile engine. That is by far the #1 use of large batteries, so they have dominated the market.
Server rooms, homepower, golf carts and forklifts are currently the only market for true storage batteries. That's not enough to justify real innovation in that market; those people simply buy lead-acid batteries and replace them every 4-6 years.
However in the past, there was a better market for such batteries. Let's take a look.
The Edison cell was specifically designed to be an electric vehicle battery, and it has a practical service life of 40 years. Though, with reasonable care, service life is basically unlimited. A number of railway museums have been able to restore 60-80 year old Edison cells simply by doing the recommended maintenance (change of electrolyte).
Our museum has a Boeing Light Rail Vehicle, and its nickel-cadmium wet cell battery can provide auxiliary power for a full hour, even today. The battery is the original one supplied with the car by Boeing in 1978.
There are over 1 million Priuses sold over the last 12 years, and Toyota has reported that only about 500 have required battery replacements.
Therefore I am puzzled when people assume "Oh, surely you must have to replace the battery every 4-6 years". History does not support that claim.