Yes, from the packet switching point-of-view, VXLAN is just a matter of sticking some encapsulation on top of an L2 frame: something that other protocols do as well.
The real difference it makes is at the control and management layer.
VXLAN evolved as a Data Center technology, so the ability to span a WAN is just an additional advantage, not the thing that drives the technology.
Consider a cloud service provider, with a data center that can contain thousands upon thousands of virtual machines. These VMs can belong to different enterprises (the cloud provider's customers), and all doing
different things, from running e-commerce applications, online shopping, ML/AI applications (like suggesting you what to buy for your wife for her birthday :-), managing calendars and meetings and so on.
In an environment like this, the 802.1Q VLAN limit of 4096 is laughably inadequate. The data center admins need a way to segment their network in more flexible and fine-grained ways.
Also, unlike say an enterprise's network wiring, which follows a hierarchical model (access -> distribution -> core), the devices in the data center need to be wired up in a more-or-less flat manner.
So basically imagine a huge flat LAN with a very large number of hosts.
Next, you also want to provide redundancy - protection against failure of individual switches and individual links. Spanning tree is of course a non-starter here: we want every link spewing data close to its max capacity. Hence the IP-based fabric, and the good things that IP comes with (like routing protocols, equal-cost multiple path support).
Next, when you get a new customer for your data center, you want to be able to deploy their VMs ASAP (in hours if not minutes), which means you want to add a new switch to the fabric without disturbing the existing switches. So, in a fabric that contains 77 switches, when you add the 78th, you most certainly do not want to spend time provisioning 77 L2TPv3 tunnels :-)
Hence the first line from Wikipedia's VXLAN page: "Virtual Extensible LAN (VXLAN) is a network virtualization technology that attempts to address the scalability problems associated with large cloud computing deployments"