Flipping
Flipping is buying a property, improving it, and selling it quickly for a profit. BRRRR shares the same front end, buy and rehab, and diverges at the end: the flipper sells and takes the profit, the BRRRR investor rents, refinances to recover the cash, and keeps the property.
The 70% rule comes from flipping, where the 30% gap between all-in cost and finished value covers selling costs of 6 to 8%, holding costs and the flipper's profit. BRRRR investors borrowed it because a 75% refinance happens to cover a 70% all-in with 5% to spare for soft costs.
The trade-off is cash now versus a rental later. On a $500,000 finished property bought at $300,000 with $60,000 of rehab, a flipper might clear $65,000 to $80,000 after selling costs. The BRRRR investor gets most of the cash back, no profit in hand, and a property with $125,000 of equity and $4,400 of rent. Which is better depends on whether you want income or capital.