They are 2 different investment approaches. Growth investing is when companies dont need to make profit now to pay dividends. Index investing is pretty much growth investing.
But dividend investing is about picking stocks which are making profits NOW and not some promise of profits in future. Dividend investors typically put lots of effort and look into the company financials and then see if they have a positive cashflow which is paid out as dividends. So dividend investors seek solace in the real cashflow.
Your philosophy about index investing is totally different. We must respect different schools of thought and try to understand their perspective.
Your definitions seem to be all jumbled up and give the impression that u have encountered these financial terms somewhere, and then imposed your own interpretation on them without finding out their actual meanings.
Growth companies are not necessary the ones that don't need to generate profits immediately to pay dividends. Nvidia and Apple are examples of growth companies that are highly profitable.
And index investing is not growth investing. Most indices are a blend of growth and value stocks. There is also a large body of academic research and empirical studies dedicated to value investing through low-cost funds and ETFs.
And sure, REITs tend to be value stocks, with healthy cashflow, and in fact REITs performance are generally in-line with value stocks performance, so I have never said REITs are necessary bad companies to invest in. My point of contention is people using dividend payout as a (primary) criterion for selecting stocks, which was shown to have no bearings on stock performance. Using Ben Felix analogy, choosing stock that pay dividends is no different from choosing only stocks with a name that start with A in your portfolio. There are great companies with name that start with A, but it doesn't mean the criterion is meaningful.
The other issue is that most REIT investors are ultimately stocks pickers, which is a fool's errand, although i understand most people have a cognitive bias to think they are special and better than most other people. And even if you put in a lot of effort and build a "diversified" portfolio of 10-20 REITs, you are still effectively betting on the real estate sector and subject to concentration risk.
And yea, there are many schools of thought and investment approaches, but some are backed by data and research, others are based on cumulation of misconceptions and appeals to psychological satisfactions.