I don't believe that the intent of require.js is to load all of your scripts asynchronously in production. In development async loading of each script is convenient because you can make changes to your project and reload without a "compile" step. However in production you should be combining all of your source files into one or more larger modules using the r.js optimizer. If your large webapp can defer loading of a subset of your modules until a later time (e.g. after a particular user action) these modules can optimized separately and loaded asynchronously in production.
Regarding the speed of loading a single large JS file vs multiple smaller files, generally:
“Reduce HTTP requests” has become a general maxim for speeding up frontend performance, and that is a concern that’s even more relevant in today’s world of mobile browsers (often running on networks that are an order of magnitude slower than broadband connections). [reference]
But there are other considerations such as:
- Mobile Caches: iPhones limit the size of files they cache so big files may need to be downloaded each time, making many small files better.
- CDN Usage: If you use a common 3rd party library like jQuery it's probably best not to include it in a big single JS file and instead load it from a CDN since a user of your site may already have it in their cache from another website (reference). For more info, see update below
- Lazy Evaluation: AMD modules can be lazily parsed and evaluated allowing download on app load while deferring the cost of parse+eval until the module is needed. See this article and the series of other older articles that it references.
- Target Browser: Browsers limit the number of concurrent downloads per hostname. For example, IE 7 will only download two files from a given host concurrently. Others limit to 4, and others to 6. [reference]
Finally, here's a good article by Steve Souders that summarizes a bunch of script loading techniques.
Update: Re CDN usage: Steve Souders posted a detailed analysis of using a CDN for 3rd party libraries (e.g. jQuery) that identifies the many considerations, pros and cons.