Is there any reason I can not use the same lan interface address (for routable public blocks) on routers at different sites as long as the router ids are unique? Or maybe even if the router ids aren't unique?
Yes, you cannot have the same LAN block IPs unless you are NATing, else your routers will have a problem. They will have a IGP advertisement to the network locally, and then they will have a BGP route to it at another site, and no matter which way they prefer, traffic between sites with the same range will catastrophically fail. If you want to do some kind of failover, you need to NAT the sites private side to the public addresses, and ensure your redundant providers are advertising your range to the internet, with one obviously preferred over the other unless there is a failure. If you are talking technically, technically you can do what you are asking, and the different router ID will ensure that routes are exchanged, but at layer 3, this design will fail.
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