Excellent post, Shanta. Thanks for highlighting the issues of externalities and trade-offs between sectors. Once we agree that governments should subsidize public goods, then two important question emerge around efficiency and equity. As I'm sure you are aware, government financing for household sanitation hardware (even if delivered through an NGO to a community) is but one way to spend on sanitation. As has been pointed out in the comments, community power dynamics may even exacerbate inequities in such an approach. In Cambodia, subsidized toilets intended for the rural poor often end up in the homes of the better-off.
Regarding the efficiency question, I am surprised that your post did not mention the private sector - except for your assumption that they're unwilling to spend on sanitation. To the contrary, I would encourage you to investigate the emerging field of sanitation marketing, where government resources are invested in the enabling environment for sanitation businesses, rather than to procure hardware. This can be significantly more cost-efficient. When local governments exhibit leadership and support for total sanitation, when local supply chains can produce, market, and deliver appropriate and desirable products, when purchase financing is available, and when consumers are empowered to choose how they will adopt safe sanitation, there is a remarkable change in the sanitation landscape.
Having said all that, it's a shame that your post is still utterly relevant and necessary. Instead of needing to be convinced why to make investments in sanitation, it would be preferable if governments were instead focused on how to optimize such investments.
Also, thanks for the great story about William Henry Harrison!
Separately, I'm also curious about your reference to Village Education Resource Centre. The link you gave is actually to the CLTS website, which is an approach that is used globally. But, a key tenet of the approach is that it eschews giving away toilets. Are you sure they were giving toilets to the community to allocate to households?