The PCIe slot on the H2 is PCIe 2.0 x4, which doesn't have enough bandwidth to saturate more than one 10G port.
This is why hobby hardware and the enthusiast market is so difficult: You can make a great product at a cheap price point and people will still complain that it doesn't satisfy their high-end niche edge case.
However, that is not due to being a cheap hobbyist board, but due to Intel, who have not provided their Atom line of CPUs with more lanes or with faster lanes.
Only the Elkhart Lake and Jasper Lake CPUs, which have been just launched by Intel as a replacement for the Gemini Lake Refresh CPUs used in ODROID H2, are the first Intel CPUs of the Atom series that have PCIe 3.0.
You can't do line rate on all ports either (limited by PCIe alone, let alone CPU for smaller packets), but you can certainly fill an individual port, which I suspect is the goal.
Are you sure about that? With 5GT/s (or 500MB/s) per lane, and with 4 lanes, that should be plenty, no? Intel adapters like the x520-DA2 are specced at 2x 10G, and use PCIe 2.0 x8.
FWIW, I was also able to iperf3 around 3.7Gbps on a X520-DA2 connected to an RPi4's single-lane PCIe 2.0.
Ethernet speeds are given in data bits per second, while USB 3.0, PCIe 1.0 and PCIe 2.0 add in their speed values the extra bits used for encoding.
On the other hand, 10 Gb/s USB and 8 Gb/s PCIe 3.0 have really those speeds. Complicated :-(
One PCIe 2.0 lane is more than enough for 2.5 Gb/s Ethernet, but not enough for 5 Gb/s Ethernet or 10 Gb/s Ethernet.
Yah, I said forwarding-- so each packet goes over the PCIe link twice.
So, to use your test-- 3.7 x 4 / 2 = 7.4gbps. I said around 7. 7.4gbps would be a bit more than I'd expect, but I'd not be shocked.