I think there is definitely room for a robot arm in the $500 range.
Sort of in the spirit of the MPCNC where the pro tools are very costly and a surprisingly good machine can be had for $500.
I respect the AR4 and the robot arms made by “Skyentific” on youtube, but I don’t think you get to something useful by taking a traditional concept and make it smaller/cheaper with plastic.
My idea is put counterweights everywhere. The elbow has a counterweight to offset the weight of the forearm at the elbow, and the shoulder has a counterweight to offset the entire weight of the arm. Then use block-and-tackle ‘tendons’ to amplify the forces from the motors to the joints. It will be relatively slow.
For extra credit, put the counterweights on a slide so they can move out and when you pick up some weight so the arm remains balanced.
For additional extra credit, use an optical feedback system to measure the precise position of everything and use that to maintain accuracy.