Both of those ways are what I said, done in different ways. PCI-in-USB3 is not a standard protocol. No matter what you do, there is no way to make it work within standard class protocols only.
> There's two other ways. One is to use a USB 3 to PCI express bridge and then functional pcie USB controller chipsets. I'm not aware of any such bridge silicon existing.
Not USB3, but this is what Thunderbolt docks/hubs do, use embedded PCI USB host controllers for the downstream ports. Which is great! But not for long: the USB-IF took over Thunderbolt and surprise surprise! USB4 includes a new USB3 tunneling mechanism but still not USB2. Yes, really. USB4 docks are expected to still have a ridiculous sidecar USB2 hub just handling USB2 duties and squeezing all that traffic into the USB2 lane all the way to the host. Because that makes sense. Of course, since PCI tunneling is still a thing and standard in USB4, at least you can ignore that nonsense and keep doing it the Thunderbolt way, but I think we're going to see fewer and fewer solutions that do it this way, and USB4 docks which do USB3 tunneling and USB2 passthrough will be a regression over TB3 docks that include full host controllers. You can thank the USB-IF for this.
> The second way is what you said, to skip the bridge and create a USB host controller that connects though via USB. Again, I'm not aware of the existence of any such silicon.
Such silicon exists, I just can't find it right now. It's another very niche thing in a similar vein to the VL67x from another manufacturer.
> There's two other ways. One is to use a USB 3 to PCI express bridge and then functional pcie USB controller chipsets. I'm not aware of any such bridge silicon existing.
Not USB3, but this is what Thunderbolt docks/hubs do, use embedded PCI USB host controllers for the downstream ports. Which is great! But not for long: the USB-IF took over Thunderbolt and surprise surprise! USB4 includes a new USB3 tunneling mechanism but still not USB2. Yes, really. USB4 docks are expected to still have a ridiculous sidecar USB2 hub just handling USB2 duties and squeezing all that traffic into the USB2 lane all the way to the host. Because that makes sense. Of course, since PCI tunneling is still a thing and standard in USB4, at least you can ignore that nonsense and keep doing it the Thunderbolt way, but I think we're going to see fewer and fewer solutions that do it this way, and USB4 docks which do USB3 tunneling and USB2 passthrough will be a regression over TB3 docks that include full host controllers. You can thank the USB-IF for this.
> The second way is what you said, to skip the bridge and create a USB host controller that connects though via USB. Again, I'm not aware of the existence of any such silicon.
Such silicon exists, I just can't find it right now. It's another very niche thing in a similar vein to the VL67x from another manufacturer.