I think your explanation is actually addressed, just not directly: the article touches on the "Government is inefficient" hypothesis (which might be fuelled either by taxes or debt; it's the incentive structure that matters, not the source of the money), but that hypothesis makes a number of predictions that are falsified:

- If the increased cost is due to government inefficiency, there is opportunity for for-profit businesses to provide the same service at lower cost, and either capture the difference as profit or compete on cost for more business. However, in practice, for-profit hospitals and schools operate at similar cost.

- If the increased cost is due to government inefficiency, then countries where the government enforces a monopoly over the service should have higher costs than countries where there is significant for-profit activity in the same sector. However, US costs are much higher and have increased much faster than in other developed countries, despite the US system being the most privatised by far.