The different L3 networks are connected by L2 networks in-between them, not just behind them. L2 doesn't disappear once you hit the router, you've still got to reach your peer's IP over L1/L2 somehow at some point. A great deal of internet peering is not even a L3 box <- direct L1+L2 connection -> L3 box connection, it's dumb L2 transport which provides the IP connectivity path for the BGP session to a more centralized router. Sometimes the path is a pseudowire doing the same with a functional MTU lower than the switched/routed path it rides on too.
These underlying paths are not always static either, just because you have 9000 today doesn't mean when the path fails to a backup alternate tomorrow the MTU will be 9000. You have to get everyone involved on the internet to agree all links should now be 9000, now you can reliably set your router's outbound link to 9000 in all cases and rely on L3 fragmentation. Until someone wants to set their MTU to 12000 :). Even when I've had paid WAN transport with contracted MTU the MTU has lowered during carrier maintenance like firmware upgrades or unit replacements and I've had to call them up saying the MTU is broken because something like NFS servers will think they can statically set a known MTU on the path and it'll stay that way, a routed neighbor on the path would make the same error in this example.
These underlying paths are not always static either, just because you have 9000 today doesn't mean when the path fails to a backup alternate tomorrow the MTU will be 9000. You have to get everyone involved on the internet to agree all links should now be 9000, now you can reliably set your router's outbound link to 9000 in all cases and rely on L3 fragmentation. Until someone wants to set their MTU to 12000 :). Even when I've had paid WAN transport with contracted MTU the MTU has lowered during carrier maintenance like firmware upgrades or unit replacements and I've had to call them up saying the MTU is broken because something like NFS servers will think they can statically set a known MTU on the path and it'll stay that way, a routed neighbor on the path would make the same error in this example.