Generally speaking, I'm not a fan (though not opposed as such either). And like you said, if the site isn't quality to begin with... definitely not.
One of the biggest pros is seeing how much demand there is for a product before you print stock. If you get hardly any pre-orders, you might decide to make it a limited edition and move on to something else
One of the biggest cons is that people are ridiculously impatient, and they don't pay any attention. Even if it's clearly marked as a pre-order, even if at the time of ordering they
know it's a pre-order, if you get enough orders you will
still get complaints from people about how long it's taking to receive the shirt, where is my shirt, why haven't you sent my shirt, I paid for my shirt where is it, I want I want I want I want, etc. etc.
It can be good for building anticipation. It can be good if you can tie it in to your marketing in a way that makes sense for your brand.
It can be good for offering options you don't ordinarily offer: for example many webcomics do pre-orders of t-shirts, and often they'll offer a complete size range for the preorder (every single size the manufacturer offers - and why not?), but only print on a more normal (S-XL, S-XXL, whatever) size range when they're printing stock.
You could offer a wider variety of colours for pre-order (Black print on your choice of White, Blue, Red shirt) then use that information to decide which colourway to use for the one you print stock of.
It'll give you your bell curve of sizing for this specific design.
It's basically free and valuable market research.
There are plenty of reasons pre-orders are good for the merchant - you just need to make sure they look legitimate to the customer.
Easiest way to do that? Pre-order discount: $3 off if you order before X date.