Bulk order single color silkscreen on a cheap tee is around $5. Totes are about the same. Dye sublimation mugs are ~$3. Not sure about nalgene-type bottles but I'm guessing in the $3-$5 range.

Is it the cost? $3-$5 per item seems about what I would expect.

I'd guess the biggest problem with tees is sizing. It's not one uniform product to hand out, so you have the added complexity of multiple inventory and people asking to swap their size.