Humorously, it's usually the mage or bard that ends up carrying it anyway, as they seldom use shields or two handed weapons. Hooded lanterns are far better than torches anyway, and you can use your 1st turn's object interaction to set it down at the start of combat if you think you'll need to hold a weapon. A 2H weapon fighter could do the same, particularly a polearm fighter since they don't need to draw their weapon (it'd be heavy to carry a greatsword in one hand all day, but nothing in the rules prevents it).It's not about "saving a silver or two". If you carry a torch in your off-hand, you're not carrying a shield, using a 2h weapon, or casting a spell with somatic components. And if you need to do that, it means you have to drop the torch, which has a chance of going out in the process, and if doesn't, acts as an obstacle for tactical movement.
There's more to torches than just their monetary cost. Think about it.