One of CPI's big limitations is that it only considers consumer goods and services (the "consumer" part of "consumer price index"). But "consumers" themselves spend a good deal of money on other things, namely health, education, and housing. SlateStarCodex had an article about that: https://slatestarcodex.com/2017/02/09/considerations-on-cost...
Do I think those who stay wealthy in real terms are able to do so via "what amounts to fraud?" No. Nor do I buy your 15-20% hurdle assertion: if your annual salary of say $100,000 was worth just 10% less each year (as in, real inflation of 15% minus 5% worth of nominal income growth, a generous income growth assumption) $100,000, over just five years, it would be worth the equivalent of ~$60,000 in year 0. It seems like a stretch to suggest that everybody but the rich are seeing their real incomes almost sliced in half every five years. Use the 20% number or a more conservative assumption for income growth and the numbers start to square even less with reality.