Are there any USB ports that allow the device to be plugged into it right-side-up and upside-down?

I doubt it since there is a physical ‘key’ blocking insertion in the wrong direction. That’s part of the standard.
Personally I don’t think that’s flawed. You want your wires each connected to the correct thing on the other side.
There’s always something that could be more convenient about most designs. If you could plug a USB in either way you could complain that you have to plug it in all the way (instead of part way) or that you have to plug it in at all. Why doesn’t it just know what the signal is? What do we have to have a wire for ?

A USB extension cable gives you more options.

Physical symmetry is easy, but making it so that the Data +, Data -, Power +, and Power – are likewise symmetrical is non-trivial, especially if you factor cost/unit into it. It would be an extreme hassle and a rise in per-unit cost to make a connector that could do that. At the simplest, you would have to make them 8-pin connectors and have crossovers… which uses much more copper. Or you could do them as a 4-conductor headphone jack, though those are easy to damage, which is why we don’t use them.

The simplest, most cost-effective solution is to not be lazy, and watch what you are doing.

I hardly think that it is an imperfect design. I also do not think there is such a thing as a “perfect” design.
It actually is one of the better relative long standing designs to have come along. The same goes for the Apple dock connector.
Considering all the connect/disconnects it goes through, I would vote it one of the better one.