Is there any disadvantage to using Oracle's Easy Connect syntax?
The only real downside is that there are a number of configuration options that you can put in a TNS alias that you can't use when you use the easy connect syntax.  Easy connect is designed to simplify the syntax for simple connections.  In order to do that, though, it loses the ability to create more complex TNS aliases that do things like load balancing/ failover or that request a dedicated server session.  If you don't need any of that, there is no downside to using the simpler syntax.  As soon as an organization has one use case that uses something that the easy connect syntax doesn't support, though, it either has to support a hybrid configuration where some things use easy connect and others use TNS aliases or it has to use TNS aliases everywhere.

Supporting hybrid configurations or changing how connections are handled can be somewhat painful depending on your perspective.  It's relatively easy for the Oracle client to handle a bunch of different naming conventions.  It's much more difficult for an organization to support.

It's relatively easy for organizations to come up with ways of distributing a single, shared tnsnames.ora file to everyone or to stand up a central LDAP server to host the organization's TNS information.  If some applications use easy connect syntax and some organizations use TNS aliases, that can be problematic when an organization wants to do things like consolidate databases or move databases from one host to another.  If an organization wants to add load balancing support, it can be problematic when some applications fail over automatically and some don't.  Someone has to track which applications are which, admins have to treat applications differently rather than being able to count on organization conventions that are adhered to across the board.  None of this is impossible, of course.  But consistency across the environment makes DBAs and admins much more productive and allows teams to support many more applications/ databases/ whatever with any given level of staffing.