Ah, but a flow battery is. The savings in weight on a flow battery are obtained because you have separated the cell and it's fuel. So instead of having to carry the entire weight and cost of a sufficiently large lithium battery(for power AND range)it carries a fuel cell sized to provide sufficient power and fuel sufficient to provide a longer range.
If you are talking a flow battery (an electrochemical device) they are all much lower energy density than current lithium-ion batteries by about a factor of 8. A Leaf battery will blow any flow battery away - which is why no one uses them for transportation. And that includes the savings from separating the electrolyte from the cell itself.
If you are talking a fuel cell, now you're on a different topic. A device that converts fuel to energy is indeed a good idea; every car on the road today has one. They work well for several reasons:
1) In most cases one of the reactants is available in the atmosphere (oxygen.)
2) In most cases the waste products can be exhausted to the atmosphere (water, CO2)
Those two factors make fuel based engines considerably lighter than things like batteries (flow or otherwise) and allow longer operation on a given amount of fuel. Hydrogen fuel cells are a promising idea although the problem of hydrogen storage has not yet been addressed. Methane storage is easier, and a direct methane fuel cell or a fuel reformer might work well there.
The fuel and lighter, smaller cell are lighter than the required excess battery that would provide the same range. Add in large high power capacitors to handle momentary high peak loads and the fuel cell can be made even smaller to provide cruise power plus a bit to keep the condenser topped off. Even lithium batteries are heavier than the electrolite in them and if that electrolite were to be replaceable you have saved the weight of the additional lithium in that second battery, third battery, fourth battery.
You cannot replenish the electrolyte in a lithium ion battery and restore capacity; the lithium is physically transferred to one of the electrodes and this cannot be "flowed' away without replacing the electrode itself (which is part of the cell.)
Then there is nano-texturing of the anodes and cathodes. Electrons are tiny little things and a smooth plate of metal can interact with a set number of them on it's surface. But nano-texture that surface and you can increase it's area by some large factor, increasing it's capacity/power by the same factor.
You can do whatever you like to the plates, and indeed such texturing can improve power, cycle life or reliability. However, nothing you can do will increase energy capacity once you run out of charge carriers (lithium ions in this case.) And in flow batteries you still have exactly the same problems - you need 8 pounds of reactants for every pound of lithium ion battery you replace. You can improve the electrodes through nanotech and whatnot, but you cannot reduce the need for reactants.
Some chemistries are reversible by adding electricity to the cell, in effect running the process in reverse(it's one of the things that distinguish the flow battery from being called a fuel cell). It is true that all extant flow batteries are in industrial power facilities, but the same was true of steam, gas and diesel power as well. Flow batteries or fuel cells(also in industry before in cars)are the two technologies that could actually improve our cars in terms of ease of use and reduction(to ZERO)in emissions. No battery chemistry can compete with either one in range or cost . . . .
Lithium ion does, in fact, out-compete the flow battery in terms of range and cost, since no flow battery can accomplish what the Leaf battery can (for example) as limited as it is.
Here's a short thought experiment.(I make a bunch of simplifying assumptions, I'm just illustrating the principle I'm talking about).
I have an electric car and I am choosing a power system. I have ten pound lithium batteries that fully power the car with a range of ten miles. I want a pack that will give me one hundred miles, so my pack weights 100 pounds. Each battery has 7 pounds of Lithium and three pounds of "fuel".
I also have a ten pound flow battery that fully powers the car, at any one time there is three pounds of "fuel" in the FB and that will give me ten miles of range. I want one hundred so I add another 27 pounds of fuel. My power supply weights 37 pounds. Since I don't mind a little extra range I make up the difference with 63 pounds of fuel, giving a total range of over 300 miles. A hydrogen fuel cell is even more effective, but hydrogen is nasty stuff(pressures/temps/flammability), electrolite would be at near atmospheric pressure and normal temps and not so nasty.
OK. Now some real world numbers:
In reality your 100 mile lithium battery weighs about 800 pounds. Your 100 mile flow battery weighs 6400 pounds. To get to 300 miles now you are at 19,200 pounds. (For reference a city bus weighs about 25,000 poiunds.) That's with a zinc-bromine battery, which is currently state of the art when it comes to flow batteries.
Which do you choose for your family car? The 800 pound option or the 6400 pound one? Or perhaps the 19,200 pound one?