The PWM greyscale is commonly used in other other display technologies like LED where controlling current is not feasible as well as Texas Instrument's DMD which is a micro mirror that can only be on or off.
Voltage-controlled current source is a pretty basic OpAmp circuit actually. There's also some tricks to turn some common voltage regulators into current controls. If your "information" is already encoded as current, you can somewhat current-mirror with a very basic BJT circuit (its not the best circuit, but if you don't care about accuracy its fine).
I'd say that current control is _more expensive_ than PWM though. PWM is just software or a 555 timer if you're oldschool, both are cheaper than OpAmps / Voltage Regulators.
Or maybe you mean, "not feasible for the costs people expect", which is probably true. PWM is just so much cheaper in practice.
I'd imagine the retail price is a combination of 'what the customer is willing to pay', and 'random'.
Some early games made that mistake. It sounds horrible in anything newer than the first A1000s.