Is it necessary to reinforce a carbon fiber steer tube?
There is absolutely nothing about requiring a compression plug inside the carbon fiber steerer in Trek's owner's manual.

Given the plethora of warnings embedded throughout that document, I'd say such a lack is definitive.  So, despite it being impossible to prove a negative, umm. no:

In general*, carbon fiber steer tubes do not need to be reinforced with a compression plug.

The myriad of compression plugs available support this assertion.  There are plugs that cover the entire inside of the tube from just a few mm under the cap down well past the stem.  There are plugs that reach down only a few mm total.  There are plugs that "hang" down inside the steer tube several cm from the cap before a short plug grabs the steer tube for a cm or so.  If the plugs were in general needed to support the steer tube, they'd all be longer than the 3 cm or so length that stem clamps onto the steer tube.  And user manuals would have warnings not to put too many spacers on the top of the stem that would prevent the compression plug from being located properly.  The Trek user manual linked above has no such warnings.  It only states that there must be at least one 5 mm spacer above the stem.

* - because there's going to be one out there somewhere that does say it's needed...