Back in the CRT days, it was possible to do pretty much what the OP described (watch active shutter 3-D on ordinary TV sets). Field sequential 3-D boxes and compatible glasses were (and still are) available for use with properly encoded VHS tapes and DVDs. There were some legit releases, but most of the material circulated among collectors. I still have a bunch of this material, and a 19" CRT in a spare bedroom to view it.
While it was the best available option at the time, the biggest drawback was noticeable flicker because the CRTs could not refresh fast enough to avoid that. However, there were options to view this material on a PC and head mounted displays, which did not suffer from this problem. The resolution was reduced as well. Using Stereoscopic Player software, I am able to watch this material on my aging Acer 3-D laptop with passive glasses, with no flicker.
I have seen some offers and Kickstarter type campains for similar active shutter device(s) intended to be used with Blu-ray 3D on a standard HD set, but from the sound of it, there are still flicker issues.
It would seem that some 3rd party would try to perfect this - they'd have a captive market.
I also have a 3-D Wizard, which is a similar device, except that it converts Blu-ray 3D to anaglyph for viewing on standard sets. Amazon had them for less than $20.00 for a while, and I picked one up to test it. It did what they advertised.