I work at a very similar place now that uses Shopify. Managing that many SKUs on Shopify is crazy painful.
The thing is is that custom ecom solutions really aren't that hard. The off-the-shelf ones are complex because, as stated above, they are trying to be everything to everybody.
I’m fairly confident I could spend a month or so writing a custom solution for a shop selling and shipping a few hundred tshirts a day that would save them enough money to break even on the software in a few years (compared to off the shelf solutions).
If I was starting my own tshirt company, I’d definitely do it.
We did an evaluation on several out of the box ecommerce solutions and none of them were able to meet the requirements that absolutely had to be there. Shopify flat out said no, they can't help us, etc.