To expand what I have in mind, it'd be a script like Gwtar, except it loads WARCs through URLs to CDX files. Alternatively, it might also load WARC files fully to memory, where an index could be constructed on the fly. In the latter case, that would allow the same viewer to be used with or without a web server. Though, I can imagine that loading archives without a web server was probably out-of-scope for Gwtar, otherwise something could have been figured out (e.g., putting the tar in a <textarea>'s RCDATA; do browsers support "binary" data in there correctly?).
While the WARC specs are a mess (sometimes quite ambiguous), I've never had much trouble reading or writing them. As for why WARC, having the option to preserve request/response metadata, as well as having interoperability with anything else in the WARC ecosystem, would be nice. Also, a separate viewer would naturally be updateable without changing the archive files themselves.