I've been following Horvath closely since he was drafted and you're right, he's only being talked about as a blocking fullback/H-back/WSTD. No one ever asks why someone with his top of the chart athleticism for the running back position has to move to fullback, especially when he was a successful running back at Purdue.
But I hold out a little hope that he'll show well enough in the preseason to get some touches, especially near the goal line, even without a string of injuries, and maybe his role can grow from there. Austin Ekeler is admittedly a top back but he's on the small side for a bellcow role and has been injured in the past though not last season. After him there's the rookie Spiller and some mediocrities. Spiller was drafted to be Ekeler's backup and maybe play third downs, but he's not exactly a bull with a nose for the endzone.
The Chargers could have let Horvath go the undrafted free agent route but they took him at the end of the draft, hopefully with a purpose more than making him just a special teams wiz and extra offensive lineman in the backfield. The current LAC coaching regime seems to have more on the ball than most, as seen by the sprinkling of White players on defense.