Wouldn't under-treatment promote resistance?

That is the orthodox view (to which I fully subscribe).

In the case of malaria there is a general consensus that under-treatment (in the 50s, Thai-Cambodian border) was the cause for resistance emergence (actually not under-treatment, but presumptive treatment - chloroquine (CQ) in small doses in salt). This was a policy recommended by the WHO (I traced the first suggestion to a paper written in 1953).

There are people trying to introduce treatment with doses below clearance. Their rationale is based on mouse models. Problem is: mouse and lab models have a tradition of not being transportable to human field reality. For instance (and this is interesting in economic terms):

Lab models predicted that CQ resistance would be maintained because CQ-resistant parasite multiply faster than CQ-sensitive parasites. We now know that this is not true (CQ-resistance falls if CQ if removed). NOTE THE UNDERLYING (wrong in this case) REASONING: something that grows faster is more fit that something that grows slower (growth, growth, growth baby). It never crossed peoples minds that faster growth might mean, for instance, killing the host before transmission is possible.

But it is interesting to see that the "growth is always good" meme goes well beyond economics....

Denying antibiotics to humans on account of the danger of building resistance seems bogus when industry is allowed to turn entire landscapes anti-biotic resistant. It is just that it is easier to let medical professionals harangue their patients than to confront big pharma and eleminate a practice that is sold as adding 1-3% growth to meat animals. If I get some chickens I will have my choice of medicated or non-medicated feed.

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."