My best guess is that it's more economical. But it may be that it's easier to install. Or perhaps there is an advantage to better bandwidth, but I'm not too sure about that.
Instead of doing a lot of research through Google and we waiting through a lot of stuff you might find on the IEEE website, I love might be easier just to ASK here because surely some of you must know the answer.
So I'm going to put this as a vote to see what kind of answers others might have and to make it more interesting.

You can vote as often as you like, but please just pick one item whenever you vote. And be sure to leave a comment to make this thread more interesting and educational.
Just to make sure everybody knows or talking about, for twisted-pair refers to the common cable that everybody uses now days to die computers together over Ethernet. This cable is often referred to as CAT-5 orCAT-6 cable. The most common collects cables that were used at one time was the RG 58 cable that required a 52 ohm Terminator.
  I think you are comparing apples to oranges.

twisted pair, or Ethernet, cable is for networks, either LAN or WAN.
coaxial cable is for TV, or cable broadband, audio/visual, etc.

for Ethernet, the 'twists' in the pairs is actually important.
inside the Ethernet cable are 8 wires, in 4 pairs(green, brown, blue, orange), and each pair is twisted at different rates.
of the 8 strands, only 3 are needed to make a connection between devices, thus allowing for expansion in the standard and piggy-backing two connections in the one line.
also Ethernet cable is predominantly used by other trades like phone guys for PABX and inter-building communications(phones, cameras) due to it being very cheap.
you can't connect, for example, two PC's together with just a coax cable.
Mark, please do some research. Before 1995 most of us were using coax for Ethernet. It was called '10-base' something and it was the TCP/IP thing used for a local network at the time. But the four pair twisted pair started to move in.
So which is better? Why? Who decided? How? When?
Using frequency multiplexing you can have four bands on a coax. Or more if you want.
Current practice on CAT5 is to only used two pair, not all four.  Instead of scolding Mark to do his research do some of your own...coax hasnt been the cable of choice since the days you mentioned...Sooty Mark. I was too harsh.
Patio is right,. Coax is compered better. But why are so many now using twisted pair?  They claim a Ethernet four pair can do up to 10 gigabits. This new technology is just changing too fast for me. 
I found this is a Google.But I wonder if he really knows.
https://www.researchgate.net/post/What_is_the_basic_idea_behind_the_twisted_pair_Why_are_the_two_wires_twisted_How_does_this_arrangement_compensate_undesirable_disturbances
Anybody out there know the real  answer?geek,

it's all good.
yes you are right, back in those days it was indeed 10base2, I still have the BNC terminators and T connectors in my network kit as we used to have game-fests where we would take our PC's to each other's places, lay the coax to all the rooms and PC's and frag each other. (good times)

I have not seen it used for literally decades and had assumed it no longer exists.
I doubt you can buy the network cards for that obsolete standard still?  (maybe in used, striped-out component, e-waste, surplus equipment stores)
Geek, are you actually looking for somebody who "knows the real answer" or do you simply refuse to accept the one you found?I have yet to find a clear, concise answer that my mind can handle. 
If RG6 coax is so much better, Why use CAT6 cable?
I can search for the above, but the answers lack authoritative proof.
Example:
Quote

For strictly TV viewing needs, the RG6 cable is esential for your HDTV. While the Cat6 can be useful, it is only required for the secondary data uses of the HDTV.

for me, the answer lies in the availability of those 10base2 cards - in other words, where are they all?

coax provides from 370 to 1,000 times more capacity than single twisted-pair.

... The biggest advantage to twisted pair cabling is in installation, as it is often thinner than coax.

If RG6 coax is so much better, Why use CAT6 cable?
I can search for the above, but the answers lack authoritative proof.

Grated, there is a lot of coax already in use by the TV cable companies. Is it any factor  the resewn they stick with coax?
Also, is not Digital better than  Analog?
And is it not true that the USA has moved from Analog to Digital TV?