Is the MAC address needed outside of the LAN?

I am leaing about MAC and IP addresses and why we need to have both of them and not just one. Say I have the following network:

Say PC 1 wants to send a packet to the Web Server. Now I understand that PC 1 needs to use two addresses for this task: the address of the Router (so that the Switch can pass the packet to the Router), and the address of the Web Server.

The MAC address will be used as the address of the Router, and the IP address will be used as the address of the Web Server.

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My question is: is there a real use for the MAC address outside of the LAN, for example when a Router is passing a packet directly to another Router (like the two Routers I circled in yellow in the above image).

I understand the benefit in PC 1 putting the MAC address (I am talking about destination MAC address of course) in the packet of the Router when inside of the LAN as I have previously explained, but when a Router is passing a packet directly to another Router, where is the benefit in it putting the MAC address in the packet of the next Router?

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