I completely understand your concerns and they are not unfounded, many online vendors have indeed painted a bad image for the online business, delivering unsatisfactory products to clients who make orders, but amongst the bad and dubious lot, there are a still few and credible ones like mine that are concerned with getting more customers and growing, hence distance ourselves from anything that can spoil our business name.
There are a couple of shops online that does that but I am afraid to order because what if the sizes of the shirts won't fit on me?
There is a solution to this, a good merchandise company can tell your size from a recent picture of you if you can send it to them.
We usually ask you -If you want a fitted T-Shirt or a free one. Depending on your preference, the best and most appropriate size for you can be determined.
And also what if the quality of the shirt is bad.
A company with bad quality products will not have recurring or frequent customers, nobody goes to where they were giving something substandard again.