Remember that creating a Google Play account already costs $20, so for the most people the distribution costs are far more than covered.

you completely ignore the #1 cost: human cost to setup your vps, manage it, backups and whatnot etc. you gotta take all costs into account.

not every developer is willing to learn and spend time configuring & managing a server. that's not the same skill set.

Human cost is not really very well measurable.

First we're talking about the free app for a good cause, so you're already providing an app for free, so you've assumed some sacrifice for others for whatever reason, and setting up a website for it may be comparatively negligible part of the whole cost to you in terms of time.

In my case I would have already had an infrastructure and knowledge how to host things, so it might take a few minutes to put some new files up on a machine used for other projects. Additional costs being pretty much 0.

And there may be benefits (even if I didn't have the knowledge and infra) like learning something new, or now having an infrastructure and knowledge that helps you save expenses or time in the future. So that would offset the costs. You can't just look at costs alone.

Google also does the work of keeping fake versions of your app out of the store.

I remember that being a problem in the app store for windows phones. Lots of fake apps that used the VLC name and logo, for example.

Android is worth sh*t without any apps. I consider providing a market for apps and managing the quality of the market is their responsibility, business expense not developers.