Sorry what? I’ve literally never heard of that issue. I run 3060s and 3070s in pre-UEFI motherboards all of the time. I’m sat next to an H61 system happily running a GTX1660 SUPER.
Where have you got this information from? I think it might be very wrong.
I’ve known of the opposite; UEFI BIOS systems refusing to boot legacy AMD cards, but that never happened with Nvidia and I’ve never heard of an old board refusing to boot a newer card. For that to be possible the card would need to deviate from PCIe 1.0 spec, and none I know of do.
Just because you haven't heard of it doesn't make it not true. Where have I gotten the information from, years upon years of answering questions on this very forum, as well as working with systems for even more years.
Read what I wrote again, often the CAUSE of this issue is that, I did not say that it happens all or even most of the time. To use your own example I've never heard of an H61 board doing it either, and I never had a problem running anything new on my old pre UEFI ASUS M4A79XTD. Its interesting you mention PCIe 1.0 because 1.0 is the spec that will almost always have issues. 1.1 is when the backwards compatibility starts.
However the board this person is using is significantly older, straight up ancient, its at least 16 years old, and many boards like that are not happy running newer PCIe GPUs. Where I have also seen this is on reasonably newer (early 2010's) prebuilt (Dell, HP, etc) non-UEFI BIOS boards. This information can be found on this forum as well as in the Dell and HP forums. I have found AMD GPUs to be more forgiving than Nvidia in this respect. Again though theres no hard and fast rule. Some AMD Rx GPUs are based upon older HD models and don't have issues, some are newer (the R5 430 is a rebrand of the R7 240, which is not based off an older HD card) and might. The issue isn't so much that the BIOS is not UEFI but instead that the legacy BIOS on the board is incompatible. Some are some aren't, the older you get the compatibility goes down.
So back to my reply to you, your initial sentence said "Yes, it should work. Its supposed to work and I’ve seen a number of PCIe 3.0 cards working in older systems like that. " I would say its highly likely you haven't seen a 3.0 GPU working in something THAT old, and I am saying that is not necessarily true because if you exclude obvious issues mentioned (PSU, cable not connected, dead GPU) if its not working that is actually a pretty good reason for it to not work, as we have seen that, especially with hardware of that age.