The US approach to student loans changed fundamentally a decade ago in 2010. The Congressional Budget Office describes how in "Income-Driven Repayment Plans for Student Loans: Budgetary Costs and Policy Options" (February 2020).

Between 1965 and 2010, most federal student loans were issued by private lending institutions and guaranteed by the government, and most student loan borrowers made fixed monthly payments over a set period—typically 10 years. Since 2010, however, all federal student loans have been issued directly by the federal government, and borrowers have begun repaying a large and growing fraction of those loans through income-driven repayment plans.

Under the most popular income-driven plans, borrowers’ payments are 10 or 15 percent of their discretionary income, which is typically defined as income above 150 percent of the federal poverty guideline. Furthermore, most plans cap monthly payments at the amount a borrower would have paid under a 10-year fixed-payment plan. ... Borrowers who have not paid off their loans by the end of the repayment period—typically 20 or 25 years—have the outstanding balance forgiven. (Qualifying borrowers may receive forgiveness in as little as 10 years under the Public Service Loan Forgiveness, or PSLF, program.)

There's a strong positive case for income-contingent loans. Because they spread out the payments over time and link them to income, the annual burden of those payments is less likely to overwhelm borrowers. Thus, students from families with limited financial resources may be more willing to use such loans to attend college, and income-contingent loans are less likely to lead to default. 

But there are tradeoffs, too. Many students presumably have some information, based on their abilities and career plans, about whether their future career is likely to be higher- or lower-paid--or whether they may be planning to leave the labor force for certain periods of time (perhaps to become a parent). With an income-contingent loan, a lower-paid career means lower annual payments and the possibility that a lot of the debt will be forgiven by 25 years after graduation when many former students will presumably be in their late 40s and still have a number of prime earning years remaining in their careers. Similarly, students who are borrowing especially large sums of money is more likely to benefit from having any remaining debts forgiven after 25 years. Thus, CBO writes:

Among borrowers who had taken out direct loans for undergraduate study, the share enrolled in income-driven plans grew from 11 to 24 percent.

Among those who had taken out direct loans for graduate study (and for undergraduate study as well, in many cases), the share grew from 6 to 39 percent. The volume of loans in income-driven plans has grown even faster than the number of borrowers because borrowers with larger loan balances are more likely to select such plans. In particular, graduate borrowers have much larger loan balances, on average, and are more likely to enroll in income-driven plans than undergraduate borrowers. CBO estimates that about 45 percent of the volume of direct loans was being repaid through income-driven plans in 2017, up from about 12 percent in 2010.

There are a variety of ways to calculate the extent to which student loans are subsidized by the government. One approach used the CBO takes into account what a private lender would have charged for making a loan with these similar risk of default. By this estimate, government student loan made with an average fixed-payment plan received a government subsidy of 9.1%, while student loans made with an income-contingent plan receive a government subsidy of 43.1%. 

I'm fine with some level of public subsidy to higher education, both by states and by the federal government,  but it's always useful to consider whether how the subsidy is administered and whether the form of the subsidy is encouraging certain behaviors more than others. The CBO discusses various possible student loan reforms: for example, removing the annual caps on repayment for income-contingent plans (so the borrower would just repay 10-15% of discretionary income without cap on the level of payment), or redefining what "discretionary income" means, requiring all student loans to be income-contingent, or require all student loans to be fixed payment. 

The CBO offers a discussion of some related but slightly different models of income-contingent repayment in Australia and the United Kingdom (footnotes omitted): 

Australia and the United Kingdom have income-driven repayment plans for student loans that are similar to those in the United States. However, unlike borrowers in the United States, borrowers in those countries do not have a choice of repayment plans: All are required to enroll in income-driven plans, which are administered in coordination with the national tax authorities. That design keeps borrowers with low earnings or large balances from enrolling in income-driven plans at greater rates than other borrowers who would receive less benefit.

Australia was among the first countries to adopt an income-driven student loan repayment system, in 1989. Borrowers pay a percentage of their annual income above a threshold. For example, borrowers who began repaying their loans in the 2018–2019 academic year paid between 2 and 8 percent of income over 51,957 Australian dollars (roughly $38,864 in 2018 U.S. dollars). The repayment rate is based on a progressive formula, such that borrowers pay a larger portion of their income as their earnings increase. Payments are collected by the Australian Tax Office, and borrowers can elect to have their student loan payments withheld from their wages like income taxes. Unlike in the United States, unpaid balances are not forgiven.

The United Kingdom adopted an income-dependent repayment policy for all student loan borrowers in 1998. As in the Australian and U.S. systems, borrowers pay a percentage of their income above a threshold. Among those who began repaying their loans in the 2018–2019 academic year, undergraduate borrowers owed 9 percent of their income over £25,000 (roughly $33,250 in 2018 U.S. dollars), and graduate borrowers owed 6 percent of their income over £21,000 (roughly $28,000 in 2018 U.S. dollars). Loan balances are forgiven after a period that depends on borrowers’ age or when their last loan was issued—once the borrower is 65 years old, after 25 years, or, for more recent loans, after 30 years. Forgiven balances are not treated as taxable income. As in Australia, payments are collected by the national tax authority—Her Majesty’s Revenue and Customs.

In Australia and the United Kingdom, the student loan repayments are done through the tax code: "In the United States, by contrast, student loan payments are collected by private servicers without assistance from the Internal Revenue Service."