I'm sorry to break it to you, but stability does not a large market cap alone make. You sent me this link:
http://www.numbersleuth.org/worlds-gold/ . It says the market cap for gold is $8.5 trillion, 7x that of USD in circulation. The USD is stable right now and has been since the end of stagflation.
A large market cap does not make gold stable; the gold market cap is much bigger than USD in circulation; thus, there is no reason to believe that a large market cap would make BTC stable.