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There's too many variables involved to have a blanket "best strategy". If you're only going to own the 30 year mortgage for 8 years, that changes the time horizon for your strategy. Then there's assumptions to be made about your investment strategy that are not certain, like assuming an index fund will earn the 7% average that has historically held true, or that inflation will be somewhere around 2-3% on average.
Maybe you end up having to sell the house in 3 years for unexpected reasons, and in that time the stock market tanked and lost 20% value due to Covid-19.
Or, you keep the mortgage for 30 years, invest the cash you saved by having a high loan to value ratio (LTV), and earn a compounded 7% interest on that cash. Your 7% gain is reduced by your ~3.5% effective interest payment, so the effective gain is 3.5%.
That's why building a spreadsheet is important to guide decision making. The variables involved are too complex to crunch in your head or to have "good intuition" about. I'll have the spreadsheet output the results of a better than average scenario, an average prediction, and a lower than average prediction to get a sense of risk vs reward potential.
Various strategies have varying degrees of risk and reward potential. Generally there is a cost associated with safety, and people are more risk averse than they are reward motivated. You feel worse losing a $100 bill you once had than being given a $100 bill randomly.
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