You say that if someone has the chops to be a real mathlete they won't need Polya's _How To Solve It_
I'll say I went to college 25 years ago with people who had competed internationally in high school and who placed competitively on the Putnam, and they LOVED Polya's book.
I think whether you enjoy seeing strategies laid out well--—whether or not you've been able to figure some of it out yourself---depsnds more on your personality than on how good you are at solving creative math problems.
Depends on required features like cross browser support, cross device support, handling pdfs, ocr images, etc. Some of the mentioned features already exist in the browser. Not sure if the browser vendors are incentivized to develop and maintain such features.