Just curious, when a paid app gets featured for free, does Apple reimburse the developer for each free download? How does the reimbursement compare to a regular paid download?
The terms of the Featured Free Weekly App listing is likely confidential and we'll never know the exact terms for any particular app.
There's probably a clause in the app promotion agreement that violation of that confidentiality would result in that developer's apps being removed from the store and a permanent dismissal from the iOS Developer Program.
My guess is that Apple offers only a partial reimbursement, like 50%.
Knowing Apple's typical behavior, they would probably say "Here's our deal, it's the same as everyone else's, take it or leave it" and the app publisher has little negotiating power. It's up to the app publisher to decide if increased download volume will offset the discounted sales price.
This would seem to be more appealing for apps with in-app purchases like Instapaper, rather than one-time up front purchases.
The only thing that keeps me from using these type of apps is that they never save user comments. I often like to peruse peoples' statements on Cnet, The Verge, etc.. (despite their sometimes rude remarks).
The app normally costs a couple of bucks, and so that price is free. As for the subscriptions, these were instituted as optional purchases to support the app when it was being developed by Marco Arment and allow for a few extra "pro" features like search, third-party API integrations, and better Send to Kindle functionality.
Give it a try and you'll even be able to try it with the "subscription" for awhile, according to their blog post. I've used the app for awhile without the subscription and still find it great (although I've been using Reading List more - Instapaper came first though): http://blog.instapaper.com/post/69803652056
If you use an eink reader like the Kindle Paperwhite, the Instapaper service is a godsend.
It's very freeing... If I stumble across a long form article, I just click "Send to Instapaper", the service rips the text and relevant images from the article, and sends them to my Kindle organized in a newspaper-type layout with other saved articles. Now I'm not hunched over at my computer reading articles, and I'm not straining my eyes reading from an LCD tablet/phone.