Btw this is a very new framework so everything is a start. So if you have better ideas about dealing with certain problems please feel free to send pull requests or start a thread on github. Thank you!
A better idea to do deal with this? Properties, like in React. You control what you pass down and every component has a clear interface you can interact with, without polluting the context. Incidentally, React has contextes, which are vaguely similar to your inheritance mechanism, but are used to implement "special" behaviours, like implementing theming across the component chains etc.
The whole point of cell is to build the simplest building block you can compose to build complex structures, and a lot of the problems faced by other traditional approaches can be tackled in a different manner using Cell.
From my experience I can build fairly complex apps without having to worry about all the problems you mentioned, they are just structured differently.
If you have time, I really suggest you try playing around with it, If you still don't like it you don't have to use it, but I'm sure it brings some interesting ideas to the table that cannot be experienced by just reading the homepage.
So while telling people to play with it is good, it's even better if you can point to a demo that illustrates and resolves the issue that was brought up.
If cell apps need to be structured differently, how should they be structured? How do you plan to support single source of truth and a large number of third party libraries written with your framework without scope clashes? I appreciate I can avoid using your framework, but that's not the point :I'm trying to express my criticism in order for you use it (or to throw it away, if you like) - I suppose you submitted your software to HN in order to receive honest feedback.