It's going to be an extremely janky or very private website if they only allow you to use it when you have 1 of like a dozen supported and approved hardware TPMs to view it.
I doubt websites will go to the trouble to keep a list of approved TPMs. It's the SSL root certs nightmare all over again and even worse. No one is going to want to deal with managing a whole new giant list of devices, having fire drill updates to revoke compromised ones, etc.