Answering my own question, I just unpacked the iOS Twitter client thinking that it must contain massive graphic resources or something. Nope: mostly frameworks, the biggest being the T1Twitter.framework - 80.1Mb of who-knows-what.

That doesn't include the 17 other frameworks all over 1Mb in size (there are innumerable other smaller frameworks) for periscope and other features.

Seems to me they could ship a 5Mb app that just wraps the Twitter web site and provides iOS native experience (notifications, apple watch, etc) and call it a day.