This is an age-old problem of the market. You will always have people who enter the market and under-cut others. That it happens in editing is no surprise, but I would propose that if the clients coming to you don't understand why you would charge more in order to produce a better result for them, then they are likely clients you don't want to work with anyway. They are not your target demographic.
Obviously editing is dealing with this issue right now due to the explosion of self-publishing. Go over to Kboards some time and you'll find writers who truly don't think they need an editor at all. We might agree to disagree but an "inferior" proofreader that charges less and therefore reads more quickly and who catches 50 errors instead of 100 is better than no proofreader at all. In that case, I see the perfect as the enemy of the good.
But ultimately your argument is that freelancers have made a race to the bottom. While I see your point, I mostly disagree. Those writers who pay $250 to line edit their manuscript will never pay your higher rate. In that sense, you (hypothetical you, I have no idea who you are) are not losing a customer when a part-time freelancer enters the market.
It's akin to Mercedes worrying about Kia stealing their customers. Kia customers were never going to buy the Mercedes in the first place.
But I agree that it's frustrating in any business to encounter clients who don't want to pay you what you are worth. Thankfully there are still writers and publishing houses who see the value. If they leave you and migrate to the lowest bidder? Well, they'll probably be back when they see the poor product that has their names attached to it.
Undercutting is one thing - one editor offering a discounted rate off the generally-accepted market rate is undercutting. Someone unskilled coming in and offering to do the same job for 10% of the rate, not 10% off, is not undercutting, in my mind. If it costs, say, around $400 to change the brakes on a car, and most mechanics are within 10-20% of that, depending on geography, type of shop, etc., and a new place opens offering brake jobs for $300, they're undercutting the market.
If Bob, who has picked up a crescent wrench twice before in his life, has no idea how to change out the brakes on a car but figures he can do it with the help of youtube comes to town and puts up a sign offering to change brakes for $50, it's a different story. If a couple people go to Bob and their cars don't immediately fall apart, but the brakes are loose and he used second-hand parts that won't last and the shoes don't actually fit the cars, and then people in the neighbourhood start showing up at the actual mechanics and refusing to pay more than $50 because of Bob, there's a problem. Actual mechanics can't compete, Bob will get a lot of business and screw up people's cars, though they might not realize it at first, the real mechanics might go out of business, and then there's a wasteland with Bob at the center and people wondering what happened.
Proofreading, and editing in general, isn't something I think of as having levels like I think you're implying. I can buy high-end cars or low-end, but there's not high-end and low-end editing. There's editing. It's correct - especially when we're talking about things like proofing - or it is not.
Unskilled editors with no experience should not be working on people's actual manuscripts without supervision. They're not, that I've seen anyway, saying they're unskilled, or that they're only worth 10% of the market rate because they'll only catch some things. They're largely, again, in my experience, suggesting that there is no difference between editors, that somehow a bachelor's degree in English is a qualification, that there's no reason to pay more. Many people, especially people with no experience in publishing, don't know that these things are not true. As you note, many people believe they need no editing at all.
It's not about getting every client. It's about it destroying the market for the actual professionals. Same as freelancing. Once there were that many people offering to work for basically or literally nothing, and there was a lot of crap circulating, the places that paid for quality had a hard time competing with the places generating tons of content at no cost. You might say that's just the market working, but where are content mills now? Tons of real jobs disappeared, now the content mills are going, and it's hard for a real concern to rebound. Physical bookstores are coming back as the ebook thing is shaking out (arguably due to the same issue), but it takes a long time for bookstores to be able to open, and then for people to keep remembering there's a reason to pay for books. No, professional editors probably don't want to work with people who don't understand the basics of editing and expect entire novels 'fixed' for $250, but that's not the core issue.