Is the non-compete enforceable if she isn't an employee of the company?
Sigh... you'd really better assume nothing. That is an incorrect assumption, most likely. I am not a lawyer. But you need one to review this piece of garbage of a contract.
which would cut out the vast majority of positions available for her expertise.
YES. You have perceived this exactly right. They may use this language to essentially force your wife into working exclusively through them.
Do not even discuss this with the contracting company rep. (a) they are not attorneys and (b) they will dismiss any questions or concerns, probably not understanding the actual law.
This article recounts "Miller vs. CTG", the aforementioned agency essentially rendering a woman - a contract technical writer - who worked through them unemployable in a large metro area.
Here's some advice. Pay an attorney to look at this contract. Based on his recommendations, line out the terms that are offensive, like this one. Sign it, initial the line outs, and send it back.
If the agency will not bend on the non compete - a reasonable non compete is to limit you from working for any client of the agency to whom they submit you, for a period of time such as up to 1 year - then I strongly recommend walking away and not looking back.
It's reasonable to say "you can't go around us to work directly for a place that you met through us for a certain time period after the introduction." It's NOT reasonable to say something like "all clients in this industry in a 100 mile radius are potential clients of ours, therefore you must work through us for all of them once you sign our paper."
You really, really, really have to check the contract wording closely, and this is a proper job for an attorney, not a layman. I suspect that the CTG case revolved around such a clause that didn't seem that dangerous to Stacy Miller at the time.
The point I am also making here is that even if the scope of the contract seems ridiculous, the agency has much more money at their disposal to make your life miserable than you do to defend your civil rights against them.
Also, simply do not listen to foolish advice from some techies to ignore the language and sign because "the contract will be thrown out as unenforceable". They are wrong. See paragraph immediately above.
And learn from this and spread the word that all agency contracts should be scrutinized closely, so that other contractors stop being screwed.