Okay, that's more clear. There are a bunch of issues to consider here.
"The creators of the design files represent that they own the copyright to the design."
If they are the actual creators of the design, then they do own the copyright unless they've sold or assigned it to someone else.
"The creators specify how the files can be used, sometimes requiring personal or home use only."
This is generally acceptable.
"Many embroiderers feel (and state openly on embroidery email lists) "I paid for it, and I'll use it any way I see fit!""
This is, of course, not the way it works. A copyright holder can sell a limited license.
"I'm looking for clarification regarding what was purchased by the embroiderer, and whether embroidery designs can be used for purposes prohibited by the copyright owner."
This depends on the language of whatever licenses were included with the sale of the files. The license should state whatever rights are included with the file.
"In most cases the allowable uses are stated on the web page where the design is ordered. In other cases, there is no such statement. Are there restrictions on allowable uses, if the website just says "Click here to purchase for $15.00"?"
Tough to say. The courts usually frown on implied licenses, so it is possible that a court could say that purchasing the files allows the purchaser to only use for personal uses absent a license to the contrary. On the other hand, the courts could say that the implied license allows any use of the file by a bonafide purchaser.
A couple of things to consider. First, a copyright holder can limit their license in nearly any way they see fit -- but, in order for a court to see it their way, these license limitations need to be in writing. Otherwise, the court may impose their own ideas as to what rights were sold along with the sale of the file. Without a written license, it's impossible to know what the scope of the license really is.
Second, what can you do about it? Unless these copyrights are registered with the USPTO, the damages that one could obtain in a copyright infringement lawsuit are limited to the actual damages the copyright holder suffers -- actual lost profits, loss of licensing fees, etc. If the copyrights are registered, then maybe it would be worthwhile to go after a potential infringer. But, then again, if the licenses aren't spelled out, who wants to take the risk of spending thousands (or, more likely, tens of thousands) of dollars to go to court?
Finally, I briefly looked over some of the case law in this area, and it's not really very settled, but an argument could be made that, even if the copyright holders have limited their licenses correctly and even if the purchaser is using the files beyond what the license allows, there STILL may not be infringement, because in this case, the "creative" part of the files may not be able to be separated from the "utilitarian" part of the files. This all gets pretty complicated in a hurry.
I guess the next question would be, who are you in the grand scheme of things? If you are a creator of these files, then it would probably be reasonable for you to talk with an attorney to make sure your licensing schemes are set up correctly. If you are a purchaser, again, you might want to talk with a lawyer to find out what you have purchased!