Would vinyl even be invented today?

A mechanical means of recording sound vibrations was bound to happen eventually in history. Who knows? Perhaps past civilizations discovered a way to record vibrations but the technology was lost. Vacuum tubes were an extension of the light bulb. Electronic amplification was sought after to both extend the range of the wired telegraph as well as the newfangled telephone.

Color television has always had the limitation of having a screen door effect. ie. the picture tube had discreet dots (and lines of resolution). The change from analog to digital was really just the means of conveying the signal. HDTVs have the same screen door effect- just more dots, like 4-5 million now versus thousands in the early color TVs. So comparing analog/digital TV to audio isn't really an equal comparison.

If I cover 3/4 of my 55" HDTV I will get even less pixels than my old Sony Triniton, but picture is still far, far superior. It is not amounts of dots but quality of the picture/process. HDTV uses the same amount of bandwidth as analog TV but delivers much more data (compression) not to mention accuracy of the colors (NTSC = Never Twice Same Color), no relections/double edges, no snow etc. If you really think that analog TV set with more pixels would perform as well as HDTV then you are in real denial.

Terabytes of digital data on an analog record....now there is some weird science.

Abucktwoeighty, I went to Wikipedia and it said basically what you said about Rube Goldberg. I always thought that Rube Goldberg was a fictitious name. I never knew it was actually a person. Thanks for the heads up.

Is taking an analog signal, converting it into a bunch of 1's and 0's that can only exist in cyperspace, and then reassemble the digital bits in an attempt to restore the analog signal as close to the original as possible, so we can then use it to listen to music, any more plausible?

Has no one listened to any music that has been produced since '87? Somewhere it has gone digital in its chain before it hit your ears. A record off of those digital masters sounds "better" to many than listening to the original digital hi-res version. Why?
All analog is fun and does have a unique experience, but it would never be invented today. It is expensive and has many incredible flaws.

I think many people enjoy the sound of a record is partially because of the high noise floor, where digital can sometimes sound just a little to antiseptic.
If you have the opportunity, listen to a great pair of speakers in an anechoic chamber. Awful. Absolutely awful, but probably closer to perfect. Humans use all the background noises around us to give us a sense of space. Analog's noise duplicates that space, digital does not have it.
It is a feeling thing, but not a sound reproduction thing.