Why is the cost of living relevant when you’re talking about debt levels? The point is simply that our debt levels aren’t that unmanageable, and we could achieve something very close to the Swedish student loan system by simply automatically enrolling people in repayment plans we already have.
Moreover, American cost of living is the same in Sweden as in the US (the GDP per capita in nominal dollars is identical to the figure in purchasing-power-adjusted dollars). You may need a car, but housing is cheaper in most of the country.
As to healthcare, making comparisons is difficult. 2/3 of college graduates have employer subsidized healthcare. For those people, you need to look at the median employee premium portion, which is $2,200/year. (There are also out-of-pocket costs, mostly for drugs, but the US figure of about $1,000 is not much different than the Swedish figure of $800 on that front).
The employee premium paid by the typical college graduate is much less than the extra taxes that same person would pay in Sweden. The median college graduate earns $51,000 in the US to start. The median employee premium of $2,200 is 4.4% of that. The tax differential is almost certainly higher than that. (In Sweden, all of that is taxed at 30% county tax, no federal. In the US, the first $12,000 is tax free, and the rest is taxed at 10-12% federal, plus maybe 4-5% state and local, plus 7.65% FICA).