You don’t spec the ESC by the battery, the motor dictates the ESC current you require. Motors draw current from the battery according to the load placed upon them, the greater the load, the more current they need to overcome the load and spin. In a plane the drag and mass of the prop moving through the air is the load. Bigger, steeper pitch prop turning faster = more load.
The motor will draw up to its maximum stall current until it cooks if the load is too great. Or until the smoke comes out the ESC or the battery runs flat, whichever comes soonest. Batteries do not PUSH current to the motors.
Think of the battery as a gas tank. The bigger the engine on the end, the more fuel it draws from the tank as you accelerate.
3000mah is large for a plane, most FT designs are set up to be light, easy to fly and use smaller packs. Picking a plane you like, then getting right pack for the planes size and weight distribution is much better and cheaper than having a huge battery and trying to fly it. Most lipo is under $20, half my FT fleet run off sub $10 packs. Even my 4s 100C quad packs were less than $20.