They are too scared of their main website being blocked at ISP's just because your small site uses their servers as a domain front.
Some people were working on encrypted SNI during TLS 1.3's development, so that TLS could encrypt server names sort of like how it encrypts all later traffic. Encrypted SNI didn't make it into TLS 1.3.
1. Have a big SAN cert with lots of names.
2. Use SNI to select the correct certificate for that client and route to the correct customer config (and therefore correct origin)
If SNI didn't exist we'd be back to the bad old days of every TLS site requiring a dedicated IP. As ipv4 exhaustion has gotten worse this has gotten more expensive. However if we're using ipv6 then hosting N listeners for N ip addresses, each with their own dedicated cert, is much more scalable.