Looked at this issue in detail, here is what I found out:

• Env variables/build parameters are in fact not expanded, even though hudson.plugins.parameterizedtrigger.BuildTriggerConfig.getProjectList(EnvVars) supports expanding.
  The reason for this is, that the Parameterized-Trigger plugin uses the dependency graph to set the downstream jobs (only past Jenkins 1.341).

• hudson.plugins.parameterizedtrigger.BuildTrigger.buildDependencyGraph(AbstractProject, DependencyGraph) is not called during
  an actual build. It's only called when a new project is created from xml, a project configuration is saved or a project gets deleted (and a few other events).
  During these events there are no env vars or build parameters around (obviously), therefore getProjectList() is called with null as parameter.

• hudson.tasks.BuildTrigger (the simple downstream trigger in Jenkins core) has no support for variables expansion at all

Possible solutions:

• check if project list contains variables, if it does, either
  • use the deprecated hudson.plugins.parameterizedtrigger.BuildTrigger.perform(AbstractBuild<?, ?>, Launcher, BuildListener) to execute those downstream jobs or
  • rebuild the dependency graph dynamically during a build

In both cases dynamically expanded downstream jobs could probably not be shown as sensible links on the job overview page. Maybe the unexpanded string could be shown with a note that it's computed during a build.

Should the use-case be supported in general?
If yes, how should it be displayed outside of the configuration page?
If yes, what's an elegant way of implementing the functionality?

Assigning this to you, as huybrechts is MIA.

JENKINS-14160 is a duplicate. Would be awesome to fix this

Please fix this bug - I need this fixed so I can fully use parameters in my jobs and not have to hardcode variable stuff directly in parameterized trigger fields.

+1 here! I'm stuck looking for this exact functionality.

Added a vote, duplicate of the ticket I just entered, https://issues.jenkins-ci.org/browse/JENKINS-23053

Yes we would like this as well.. seems it works for the "Build" section but not the "Post Build" section!

It would be awesome if this can be fixed. It doesn't seem to work in either 'build' or 'post build' sections.

It is not fully addressing this issue but i have added ability to resolve default values of parameters. This is enough for me because i am using parametrized trigger plugin in conjunction with inheritance project plugin. Thank you Fred G for your analysis. It was helpful.
For some reason when inheritance build configuration is changed the downstream job link does not get updated but build is triggered.
https://github.com/J-cztery/parameterized-trigger-plugin/commit/9fdaca08fd480f5d01399f2e03a2fa2c1170d3bd

Still hasn't been fixed in Jenkins v1.634

There is workaround. In the Build section you can add "Additional Step" and then add "Trigger/call builds on other project". Then you can use variable in the name of the next job. See picture.

This workaround works, but it also causes the Multijob view to not show the triggered job. Are there any plans to correct this?

This workaround does not work for me, any other possible solutions?