Why did tv go digital?

The only reason is profit as always.

Digital allows stations to put multiple signals in the same frequency space of one analog channel.

More sub channels means more commercials more commercials means more money.

Same reason trains are not steam powered anymore. Outdated technology.

digital has a better picture, and takes up less space, so the federal government can auction off the frequencies to cell phone companies

Because digitally formatted (and compressed) data takes less "space" on radio channels than simple raw analog video.

The digital system can send many apparent channels on each radio frequency, using a time division multiplexed system.

And, it can support HD - which it that was based on the analog format would have cut the number of possible channels down by a large factor, as it needs to send vastly more information for each image.

Plus the overall image sharpness is far better with the digital system; the same as with computer monitors and now CCTV steadily moving from analog connections to digital.