A WAN connection should truly only occur in large environments. WAN is massive in size where it is almost always slower than a LAN. The further the distance, the slower the network.
One of the biggest disadvantages of utilizing a WAN is the cost that it can incur. Having a private WAN can be expensive due to the technology required to connect 2 remote places.
WAN connection is generally harder to set up, as it requires various connection between wireless technologies such as cellphone towers and satellites. Therefore it requires a high level of professionalism to setup and maintain.