Exponent is not the right fit if my project requires custom native modules.
Which ones? :) This will be less of an issue after we release eject: blog.getexponent.com/answered-on-slack-ejecting-f…
Which other use cases might Exponent not be a the right fit for?
The only other use case I can think of is if you want to deploy apps privately and host them on your own servers. Currently we (well, Amazon) host your JavaScript bundles and assets, but this may become optional in the future.