As a University student I will try to answer your question. No, I don't think it is possible for every individual to get their college education paid for without a loan.
For starters, most families do not have enough saved up for their children's education. Second, It's not impossible, but still difficult to obtain scholarships, bursaries in the amounts needed to totally pay for post-secondary education. There are many bursaries and scholarships out there, but being able to find them and apply to all of them may be more work than they are worth. Many have certain criteria you must meet, so often plenty of students do not qualify (at least that's what I kept encountering).
Third, in order for the student to have amassed enough money for college would mean they would have had to work while in school and during the summers. The employment rate is rather low and I'm not sure how easy it is for students to find work while in school or for the summer that pay minimum wage or more. If you have to work while in school, it will have an effect on your grades and the amount of time for studying, hence possibly effecting your chances of gaining a scholarship. If you or your family is not considered low-income, you may be unable to apply for bursaries as well.
The cost of post-secondary education goes up every year, as I said earlier, being able to come up with tuition plus books may be rather difficult for most students.
If a student takes a year off to work full-time before going to college, they may end up deciding to continue working and never go to college, or they may not want to go because their friends are already one year ahead of them, etc.