I believe you're describing a port for a balanced bus with a pinout such as this:
- Gnd
- D+ or D-
- +5v
- D- or D+
- Gnd
If so, yes, that is technically possible. A specialized IC would include a demultiplexer (four bidirectional MOSFET switches, for a total of 8 MOSFETs) to direct pin 2 to either the D- or D+ line, and pin 3 to the other line. The demultiplexer would flip one way or the other based on sensing the voltage on pin 2 vs pin 4. If idle, the port would try one polarity, send out a message and see if it is acknowledged. If not, it would switch polarity and try again.
(We would not use rectification because diodes would reduce the signal level and demodulate any AM interference as the cable acts as an antenna.)
The plug would have just five contacts on just one face. The receptacle would also have 5 contacts, but they would be forks, so that they contact the plug's contacts regardless of its orientation.
Now, a connector with 5 fork contacts is not that much cheaper than a two-row connector with 10 contacts, 5 at the top and 5 at the bottom. With such 10-contact connector there would be no need for a demultiplexer because pin 2-top would be connected to pin 2-bottom through a PCB trace. That saves the cost of a demultiplexer.
Extending the concept even further, why not also have a 2-row plug? Now you have twice the current handling (because there are 2 pins in parallel for each line) and twice the reliability (because even if one side is not making good contact, the other side is). Now you're back to the USB-C solution. Which doesn't sound so back after you consider all the above, doesn't it?