Why doesn't someone invent the liquid battery for an electric car/plane/heli. Then you could just go to the bowser and drain/fill with freshly charged liquid and go on your way, just like one does with fossil fuel transport.
Well, there are a number of primary cell solutions that work in this way. A primary cell is basically a battery that can't be recharged again. Some of them can be mechanically "recharged" by replacing the material that has produced the electricity.
One such rather interesting cell is the Al-Air cell. It's basically an Alu cathode and an Air anode that produces a lot of electricity. However, it does consume the Aluminium, so once the process is started (often by introducing the saline solution) there's no stopping it. There are a couple of companies that are experimenting with these primary cells where you can quickly just replenish the Aluminium, i.e. refuel, and then be on your way again. Al-Air cells have very good power density. There are other primary cell solutions as well.
Time will tell.
But as for pushing the power consumption up the chain, nuclear powered energy is much much more efficient at producing electricity than drilling for oil, shipping it across the world, refining it and the finally have a super-inefficient combustion engine turn it into propulsive power. Even if electric motors and batteries were
less efficient than combustion engines, it would still be a less lossy way to produce all the energy you need in one place than do it at the end user.