If you use an archetype to create a project, then you get only what the designers of the archetype have provided. I have often found that many Java EE archetypes don't include the test directory structure. But there is nothing that says you can't create the directory yourself. My best suggestion is to create your own archetypes that contain everything you want. That's what I do, then I get a POM with all the settings that I want, a lot of boilerplate code, and lots of other things that I typically add to any of my web projects, all at the push of a button.
In Maven you can move any of the folders to different locations. But you do so at your own peril because some plugins are not as good as looking up the configured location, instead relying on the default location.
Also, the absence of a test directory doesn't mean that something is amiss. Perhaps the archetype authors assumed that it is too difficult (or not possible) to write unit tests for that kind of web app (yeah, bad assumption). There are a lot of other conventional directories that are also missing from most archetypes.