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One shouldn't expect to systematically beat the market without privileged information. But even "trying to beat the market" (depending on what exactly that strategy entails) or doing what you describe is often better than what most people do in terms of actually growing their savings. Financial securities (especially stocks) have high enough long-run expected returns such that a "strategy" of routinely accidentally slightly overpaying for them and holding them still results in a lot more money than not investing at all.
Not investing is far worse than shoving your money into random stocks and committing to reinvest all dividends for the next 50 years.
Is there absolute utilitty maximisation in portfolio diversification or is that just a risk control mechanism? Could I pick one random stock and put a whole lot of money in it? I suspect I may be commiting the law of large numbers here (or the gambler's fallacy).