* allows a user who has not signed in or paid to connect to the local bitcoind (to download blocks etc.) or to view the landing page that contains the payment info. Not more, not less.
That part is a little impractical, you'd have to allow users to access the most common spv servers and online wallets since most will not be running around with full nodes. It'd be more likely that a client is running electrum or simply using their circle account than that they'd be going around with bitcoind installed on their laptop or worse cellphone.
I don't know enough about Electrum (afaik. it requires some kind of custom remote server), but accessing web wallets is out of scope for sure. Proper SPV wallets such as bitcoin-wallet on Android are able to connect to bitcoind instances.
As Bitcoin-core can prune the blocks on disk, I don't see any reason not to use a proper client instead of something that relies on remote trusted third parties. If you want to add extra stuff (such as connectivity to a local Electrum server or similar - or even connecting to web wallets or other external services) be my guest, but it should at least be configurable service by service - these tend to die out from time to time due to security fluctuations (just look at this thread here and check how many links still work)...
At least bitcoind-access-only mode has to be provided and working, if other services are also provided (e.g. you'd likely need to resolve DNS queries to even let users contact circle.com), they need to have an off-switch.
So a couple points to be a little bit realistic here:
1. The best way to implement a solution for this would be to use one remote server-side application, and a client-side application that would run on a router. The client would basically forward all requests to the server, and the server would handle payments, authentication, and re-routing.
2. If you wanted to implement this as just a client side application where anybody can use it, that would be possible too. However, it would require communication with the internet in order to perform bitcoin transactions. Furthermore, it would be unreasonable to not use an external service for handling bitcoin payments. Building a bitcoin payment system from scratch would be a horrible idea... way too much time and effort to try to reinvent the wheel.
3. I seriously doubt you can find good software engineers who are going to want to build this as open source. Or if they did, the reward would have to be way way way more than 20 BTC. An app like this wouldn't be too difficult to make, but it would be VERY time consuming. There are a lot of moving parts involved. In real life, something like this would most likely cost at least several hundred thousand dollars to develop.
1. I'm not so sure why the server should handle routing, otherwise I don't see how a DD-WRT router shouldn't be capable of most of the legwork (except for handling more complex payments/cryptokeys in case a more modern approach is taken than "pay x amount and once confirmed (or marked non-RBF), you get network access for y minutes or z MB of traffic credits"). In the end it doesn't matter much, since there will have to be a trusted full node somewhere in the local network anyways, so running a small server there won't do much harm I guess.
2. No, read through this thread and on the concept of payment channels. Also the point of Bitcoin is to be able to handle your own infrastructure - bitcoind is more than capable of handling payments securely and it can also submit arbitrary payments to the network. The back-end server would be online anyways of course.
3. Maybe in Silicon Valley it would? I personally don't see a big market behind this, which is why I'm not going to start a company and collect funds to develop this stuff - if however someone wants to: feel free to do so! If you want to receive money from me as a reward/bounty/donation/whateveryoucallit, I think I was quite clear under which circumstances I would be willing to hand over the equivalent of several hundred USD in current value (which is still the SAME amount of BTC by the way that I offered years back when it was about 20 USD!). Joinmarket for example is a project that is getting close to the maturity that I'd expect and I doubt that it cost several 100k of USD... Anyways, thanks for your opinion.