The expense half may be cheap, but does the time count as wages? That could be non trivial.
In my case, I leave the house an hour before work, but I have some errands I run. When does my "commute" begin? If I wanted to cheat and bump my pay, drive to a park and ride near work and show up on the bus, which wouldn't be that much longer than normal. Then show my employer the public transit route from my house that would have a 2.5 hour transit time, and claim the extra 3-4 hours as pay.
It's such a tricky gray area. On the one hand it is unfair to lose hours to a commute on your own time, on the other it creates ways to cheat the system that should be difficult to audit, unless I give my employer permission to track me, which seems unreasonable.