Beyond that, it's DIY, with a set of strong servos and a few budget microcontrollers/motor controllers, from Alibaba, and...a 3d printer to manufacture the rest, for something like an arm.

Don’t think it’s cheap nor a “platform” but maybe it’s enough to get you started ;)

He just recently put out a video on making a carbon fiber arm piece for it.

Now that I'm leaving Academia I was trying to figure out how to get a robot arm so that I can continue doing stuff at home. I think an approach like the one here would be good: https://www.trossenrobotics.com/aloha.aspx. A single robot would cost 5k. You could also just buy Dynamixel servos and build it on your own, shouldn't be too hard with 3D printing ~ closer to 3.5 or 4k with that.

You could try to go cheaper by building a dynamixel servo on your own. I would not recommend this, the main difficulty is the controller which requires a lot of tuning, which is what you're paying for when you buy Dynamixel. But the raw parts of a servo are only around 50-100$ I'd guess.

Lastly any arm you build this way is going to be position control which is very different from the human arm that is torque controlled. Trying to get torque control on your arm is all the rage on Youtube these days, perhaps because the motion seems so lifelike. To do that you need to build a Quasi Direct Drive Actuator which is a BLDC servo with a low gear ratio and then try to centralize all the motors to reduce inertia. There is no accepted solution to do this, but the best results come from cable driven mechanisms like AmbiDex. Basically building a human like robot arm is a huge research problem on its own, and if you want to focus on intelligence best avoid this.

Is it really just tuning? That seems like something that would pay off for an aliexpress copycat. A servo is pretty simple/cheap to build, right?

I guess there are only a handful of us who really want high-accuracy, high-torque component servos...