You don't have to sign up with Coil to earn. There are other wallets that are on the Interledger network such as Uphold and Gatehub that can give you a payment pointer to put into your site's HTML. If you want your earnings to be converted to BTC that's possible I think.
However, there's no reason for me to have an account anywhere in order to receive bitcoin. All I need is a bitcoin address.
I don't want to sign up with Coil, Interledger, Uphold, Gatehub, or any other random third party, in order to receive bitcoin. And there is zero reason why I would have to.
So that you can make payments to someone else regardless of whether they want to use Bitcoin or not.
I believe Interledger is the right level of abstraction for this, in the same way that you wouldn't want your email server to have to know or code against the lower protocols, e.g. Ethernet or WiFi, but only IP, TCP and SMTP. This way your email server can EHLO any email server, regardless of the network topology or underlying protocols.
Interledger does the same for payments.
I see no evidence that Interledger can be used for receiving money without having to set up accounts or run software. Plenty of evidence to the contrary.
As I said before, to receive bitcoin from one of these systems, there is nothing I should need to do other than advertise my bitcoin address. Anything more than that, and the system sucks.
Correct.
What you want requires support in the user agent (web browser) though.