Do you even have a basic grasp of economics?.
Prey tell, what are your qualifications on the matter?
Not everybody can have good jobs, it doesn't work that way.
Regardless of how "lazy" somebody is, only a certain (small) percentage of people can have "good" well paid jobs - don't tell me you are one of those people who think "with the right attitude you can do anything" rubbish?.
I didn't say anyone could do anything, just that everyone has the potential to do something decent. Largely, this requires accepting you're going to need to use your brain for a moment, and learn some skills, but there is no underlying reason why people with considerable amounts of free education are not capable of that. Everyone has the opportunities, some don't take them and some don't want them.
As how would it work if EVERYBODY had the right attitude, learned new skills & self taught?, do you think jobs which required those skills would suddenly magic into existence? - or would we have a large population of over-qualified call center workers/shelf stackers?.
For the record I've worked in a call centre for some time after graduating, and I wasn't paid minimum wage. The pay scale of such a job ranges from pretty poorly, to semi-decent based on how well you can actually do the job. Most people sucked at their jobs, and the vast majority of them were fairly young.
I moved on to technical support role, working with two young ladies who mostly sucked at their jobs and young man who was pretty decent. The company was always interested in good staff, and within 3 months they'd created a position for me finally land my first dev role, promoted the other guy, and wasted a good bit of time trying to train the two totally uninterested females. Of our replacements, one of them were fired for leaking the password of one of the UKs largest footballs teams FTP details over IRC, whilst the other was promoted within a year. The young ladies still sucked and were never promoted.
I soon left, and discovered a common theme. Everywhere you go, there are always people who don't particularly care too much about their job, and don't particularly try too hard, and almost everyone is desperate for good staff, and currently hiring those people whether they're advertising or not. My current company are offering 1k referral fees for mid level Perl programmers, and have a number of vacancies.
I'm not trying to argue that there are enough good jobs for everyone, just that in my admittedly limited experience, companies have a hard time filling the roles they are looking for, especially those that require a reasonable level of competency, and often these same companies hire a number of substandard employees just to make up the numbers. So yeah, I do believe if you want a better than minimum wage job, and are willing to work for it, you can get it.
The argument _does_ rely on a level of people being inherently lazy (or stupid, but I believe stupid comes from lazy), and if we ran into the problem where there were no more lazy people, then year, maybe we'd have a bit of a problem (probably, we'd have an awesome German like export culture, but thats by the by). Your counter argument relies on a theoretical world where everyone works hard, one that from my experience, just doesn't exist. However, if you accept some people are lazy, what is the basis of the argument that they should be rewarded equally to someone who isn't?
That's without even opening the massive can of worms regarding inequality of opportunity.
I already mentioned there was a glass ceiling (though I believe that only makes the path more difficult, not impossible). I'll even agree that I don't particularly think there is a proper equality in renumeration for all staff (though what a Government can do, and whether or not it's their place is a huge argument), however I don't believe the problem lies heavily with minimum wage positions, and I don't buy the idea that people working in those are often heavily qualified in other areas.
For the record, I'd be all for defining the minimum reasonable living wage, upping the tax allowance to that, making minimum wage reflect that. However the likely outcome is that skilled workers will expect wage rises, services will become more expensive, and you'd then be stuck again with a minimum wage that is too low. The solution would be far from elegant.