or how many services like streaming, banking, gaming will restrict, block, or otherwise treat the connection differently because the traffic now exits via a datacenter or VPN IP/ASN.

I did run into this and claude implemented a work-around (see step 8) to route some traffic through the normal exit IP for those special use cases. So far I've only run into this problem with 3 services (Ring, Blink, and Paychex). Surprisingly none of the streaming services seem to care (Netflix, Amazon, Apple TV).