Arduino Web Editor is not completely open source. Some parts of it are, most likely because that was required by the licensing of the code they are based on.
It's unfortunate if they have to charge for it but it makes sense to me because they have invested a huge amount of resources into this project over the course of years. There will be significant ongoing costs to pay for the servers and bandwidth to keeping it running. The closed source nature means that the community can't significantly contribute to the work. They don't even have the bug tracker open to the public. Arduino boards have frequently not been available from the store, probably due in part to the Arduino vs Arduino shake up so that can't have helped their income.
I haven't been a big fan of the Arduino Web Editor project because I have seen it as taking resources away from development of the standard IDE at a time when there were significant issues (primarily the early days of arduino-builder). In a way I'm glad if it can start generating some of its own resources.
I'm not familiar with Chrome OS. What sort of barriers are there to making the standard IDE run on it? If possible, that seems like the best approach by far.