MTUs of larger than 1500 bytes are also possible, and are quite frequent when using Ethernet-based WAN protocols.
There are a number of reasons why this might be desirable... L2 adjacency from site-to-site over a shared network (the Internet, for instance). That's known as a layer 2 VPN. Psuedowires are one way of accomplishing this...basically, you create a psuedowire between two interfaces on a router and whatever goes in those interfaces is encapsulated (usually within MPLS) and then transmitted over the network at large and output from the interface on the other side. It functions exactly as a direct network link would.
Direct IP (L3 VPNs) is fine for most applications, but there are certain things that can't work with it. VMotion artificially requires L2 adjacency between hosts. So, if you want VMotion across sites, you'd need a L2 VPN. Even with VPLS/MetroE and separate VLANs, it may be desirable to extend this via encryption. So you would encapsulate your VMotion traffic inside MPLS over GRE over IPSec and then send that across the WAN link, rather than simply extending the L2 VLAN across the WAN link.
The tech wouldn't exist if there weren't a few applications for it. Mainly, it exists so that you can transport ANY L2 protocol over an IP link...the fact that it works with Ethernet is incidental.