Why does a gigabit/sec Internet connection via cable (coax) not offer symmetrical speeds like fiber?

There's no limitation of coaxial copper cable as a medium that would require it to be asymmetric. So it's not about the physical medium per se, but about how cable TV companies (DOCSIS cable modem ISPs) have designed and built-out the rest of their infrastructure over the last 50+ years.

Cable ISPs' cable infrastructure carries a lot of baggage from the Cable TV days. Cable TV, before DOCSIS cable modem internet service became a thing, didn't need much upstream bandwidth. All the upstream was needed for was to authenticate the cable descrambler set-top boxes, authorize occasional pay-per-view transactions, and maybe do a few minor "interactive TV" things, like letting you check your cable bill from your descrambler box.

So typically, only frequencies from 5MHz to 42MHz were used for upstream signaling, while all the frequencies from 54MHz to 1GHz were used for downstream. So the upstream bandwidth was only about 4% the size of the downstream bandwidth.

Because they choose to place the "split" between their upstream and downstream frequencies around 42-54 MHz, all their filters and amplifiers installed on all their utility poles and equipment boxes and "headend" facilities are all designed around that very lopsided split. Also, every DOCSIS cable modem and cable TV set-top box and "cable ready" TV tuner are also designed around that split. So moving the split to up to a higher frequency to allow for higher upstream bandwidth would be a huge, expensive undertaking.

By the way, I'm speaking about North American standards/conventions here; Europe is a little different, with a slightly higher split. I should also note that since the cable operators' infrastructure was built around sending the same TV signals to all houses, they basically just run one cable to your neighborhood, and then use passive splitters and dumb amplifiers to split that one cable to all the houses in your neighborhood. So you don't have a dedicated coax cable directly from your house to their headend equipment, so they can't change the frequency split on a house-by-house basis.

Under current DOCSIS standards for how the upstream signaling is done, the most bits-per-second bandwidth they can squeeze out of their limited upstream RF bandwidth is only somewhere around 35 Mbps.

That's why you can't get symmetric DOCSIS service above about 35Mbps, and why even if you get gigabit downstream service, its upstream is only going to be 35Mbps or below.

If you call for business service from a cable ISP, and ask about packages with upstream speeds above 35Mbps, they have to build out fiber optic infrastructure to your business because they just can't do it with their existing coax cable infrastructure. Not because coaxial copper cable has a limitation, but because all their equipment up on the utility poles between their headend and your business was designed around a very lopsided division of upstream vs. downstream frequencies.

Short answer:

Yes. This is an artificial limitation that companies apply on purpose.

Long answer:

There's no specific limitation in copper, but there is a limit to the frequencies you can push into copper and have it come out the other end as readable data.

Whether or not you make a connection asymmetric just depends how you want to use the bandwidth that you have. If Cox really wanted to, they could offer a package with 500mbit up and 500mbit down, or split it the other way and offer 1GB up and 30Mbit down. The vast majority of consumers want the faster part to be the download though, so that's what they offer.

The main difference between Fiber and the type of Coax connection that Cox use is that Fiber is a Point-To-Point system, whereas Coax cable tends to be a ring network, star network or some other topography where at the very best, you're sharing bandwidth with all your neighbours, and at worst with everyone in your town.

Not that this fact in itself means that they have to allocate more to down than up, but it does mean that there's almost always going to be competition for spectrum and the ISP is more likely to be constrained by demands on your local copper wire more than they are by their actual connection speed to the outside world. Faced with the fact that there is going to be contention on your wire, the safest and least impacting option is to limit upload speed to prevent the local area getting too congested.

With Fiber, you're more-or-less connected directly to your ISP on a one-to-one basis. There's nobody else trying to communicate on the same frequency or sharing your line, so they might as well leave it uncapped.

However, this only tells half the story.

Another reason ISPs like to cap upload is cost. It's becoming less and less common, but some ISP peering arrangements allow ISPs to download for free, but charge for uploads. So your ISP limits how much you can upload in order to limit their own costs.

And finally, they do it so that they can up-sell you on to their business tariff. The reasoning goes that if you want a lot of upload you're probably running some kind of server, and if you're running some kind of server you can afford a "proper" business connection with uncapped uploads. If you can afford to pay more, and they can engineer a situation to make you pay more (without annoying too many of their customers who are quite happy with crappy upload speeds and simply don't know any better) then they will absolutely do so.

At the moment, Fiber is a new technology and they want to attract enthusiasts and prosumers to buy it, so they aren't really offering asymmetric fiber connections yet. They will come though, as soon as someone figures out they could be selling the same product badged as "business fiber" for twice the cost.