I have some additional test results using, both, a noname PCIe-to-PCI bridge adapter and a Startech PCIe-to-PCI bridge adapter. I also tried the Startech USB 3.0 PCI card with kernel 4.15.0 and on another system with 4.4.0 and it still does not function in linux. The lspci terminal function shows the bridge and the NEC USB 3.0 card on the Startech PCI card, but when plugging in a USB HDD nothing shows up.
On my AsRock 939Dual-SATA2 opteron 185 motherboard, using USB 3.x cards in either of the PCIe-to-PCI bridge adapters yielded no visible HDDs attached to the USB port. Linux sees them, but for some reason there is no USB drive shown in the Disks app, meaning there is nothing to mount.
On another computer, an Asus i915GL based board with a 64-bit Prescott P4-3.8 GHz, some combinations of bridge adapter and USB 3.x cards did yield a working USB HDD. For these tests, I am using a Samsung 870 EVO SSD connected to a Ugreen 3.1 gen2 SATA-to-USB adapter. Some base numbers before the numbers of interest.
Internal USB 2.0 ports (intel something):
Read = 40 MB/s
Write = 32 MB/s
Renesas NEC D720201 USB 3.0 card connected to the PCIe port (1 utilised data lane):
Read = 196 MB/s
Write = 161 MB/s
ASM1142 connected to the PCIe port (2 utilised data lanes):
Read = 395 MB/s
Write = 258 MB/s
ASM3142 connected to the PCIe port (2 utilised data lanes):
Read = 388 MB/s
Write = 264 MB/s
when connecting the USB drive to the USB-C port on ASM3142, the results are shockingly low. Why?
Read = 44 MB/s
Write = 40 MB/s
Fresco FL110: Linux doesn't find any HDD when connected
VIA VL805: didn't document the results or didn't test. SCSI2SD software doesn't work with any VIA-based USB 2.0/3.0 controller card I have tried.
Now let's compare the results of the controllers
ASM1142 connected to the the noname PCIe-to-PCI bridge card:
Read = 105 MB/s
Write = 39 MB/s
ASM1142 connected to the the Startech PCIe-to-PCI bridge card: cannot, Startech slot is x1 keyed only
ASM3142 connected to the noname PCIe-to-PCI bridge card: Linux doesn't find an attached HDD
VIA VL805 connected to noname PCIe-to-PCI bridge card:
Read = 104 MB/s
Write = 37 MB/s
VIA VL805 connected to the Startech PCIe-to-PCI bridge card: doesn't work
Renesas NEC D720201 connected to the noname PCIe-to-PCI bridge card:
Read = 101 MB/s
Write = 36 MB/s
So far, all the read/write speeds for a USB 3.x card on the conventional PCI bus are about the same, but the magic combination comes next.
Renesas NEC D720201 connected to the Startech PCIe-to-PCI bridge card:
Read = 115 MB/s
Write - 79 MB/s
If all you care about is the read speed, then it doesn't matter much which USB 3.x card you use on the PCI bridge, but if you want to double you write speed, you need the NEC D720201. What is most interesting is that the PLX bridge chip model on the Startech PCIe-to-PCI bridge card is the same as on Startech's stand-alone USB 3.0 PCI card. The NEC USB 3.0 model is also the same. So why doesn't the Startech stand-alone USB 3.0 PCI card work correctly in Linux, but the NEC w/bridge adapter does?
The natural next step in benchmarking would be to try this combination Startech PCIe-to-PCI bridge card w/NEC D720201 in a motherboard which forces the PCI slot to 66 MHz. How much more performance can we get out of it? Also interesting would be to test the Renesas NEC D720201 USB 3.0 card on a PCI-X slot, but I never bought one of those Startech PCIe-to-PCIx bridge adapters when they were still available. I think they were $200 at their lowest point.
Edit: Unfortunately, that magic combination doesn't work in my As939Dual-Sata2 board. I checked twice. Ubuntu sees the bridge and the USB controller, but no HDD.
Plan your life wisely, you'll be dead before you know it.