Helicopters are proof you don't need wings at all.
However, short wings (left right), no matter how long (front back), are less efficient than wide wings. You can see this from basic physics without having to understand anything about how wings actually work.
Consider a plane in straight, level, and steady flight. The net force on the air is to push down on it by the weight of the plane. That force is produced by imparting momentum downwards on the air immediately surrounding the plane as the plane flys by. Momentum is mass x velocity. In this sense stubby wings and wide wings are equivalent. You can get the same momentum by pushing a little air a lot (stubby wing), or a lot of air a little (wide wing).
However, consider the power requirement. Power is proportional to the square of velocity times the mass. Therefore, pushing a little air at high speed takes more power than pushing a lot of air at low speed. Stubby wings transfer more power into the air for the same lift. This extra power shows up as higher drag, which ultimately requires more pushing from the engines to overcome.
Wide and thin wings are best for efficiency, but there are structural limits and other trade offs. Note that wings of gliders (where efficiency is very important since the power comes from altitude loss) are very wide, but thin in the other two dimensions. They also can't carry much payload, in part because the wings are too fragile to support it.
Everything is a trade off. Jet fighters have other important criteria, like maneuverability, high top speed, good cockpit visibility, small radar cross section, etc. It is often useful to give up some efficiency in return for these other features. It all depends on what the plane is supposed to do.
Take a look at the F104 as a example of stubby and thin wings. It was fast, but also very tricky to fly, with several pilots lost due to inability to control the plane.