Why should my taxpayers dollars be going to pay for remedial classes for subject the students were too lazy to deal with in high school?
This isn't the real problem... meaning "lazy students". In fact, the remedial classes are more likely because either the high schools did not teach the subjects adequately, or the students are simply unable to do the work. "Lazy students" shouldn't be able to be accepted into a university in the first place, or more importantly, shouldn't be able to pull off the kinds of grades in high school that can get them accepted in the first place. Grade inflation is pervasive, and the current strategy of "teaching to the test" so that the highest priority is having students pass the standard of learning tests (which is what they are called here in the Commonwealth of Virginia) doesn't mean we are turning out students who are suited, or even capable, of moving on to college.
The idea that everyone must, or even should, go to college is wrong-headed. There are a lot of people who are simply not able to work at that level. Furthermore, there are a number of other perfectly fine ways to be educated that can result in successful people with marketable skills other than universities. In fact, for a lot of fields, a university education is quite orthogonal. While a lot can be gained from a general university education, pushing someone who is not capable of this level of work, but who could succeed and prosper in a skilled trade, into trying to get a degree might be a disservice.
The biggest problem here is that a high-school diploma means far less than it did in past generations, and that's where we are really failing. The need for education is always increasing, but the education system itself is not improving to match the need.
Welders, plumbers, electricians, carpenters, machinists, etc.... these are people who can command good salaries, find lots of work and be very productive and successful people, but whose education and training don't necessary fall into what a university can provide. Furthermore, a lot of service type jobs honestly don't require a university education, and while such an education would certainly provide value to a person's life, undertaking the incredible expense and risk of trying to obtain a degree is often not going to be worth it, at least at the costs as they are today for a traditional four-year university degree.