It isn't conventional wisdom, just a conventional loan product. An important element in the lending process is a ratio called Loan-to-Value (LTV), which is the ratio between the amount of money a bank will let you borrow compared to the value of the property you're buying.

Banks generally do not like the idea of risk, so they'll usually find a way to ensure against a bad investment, for example you borrowing a bunch of money and not paying it back. One way to ensure against such a bad investment is to create an agreement that says "we'll let you borrow this money; but if you stop making payments on the loan, we (the bank) get to kick you out of the property, sell the house, and use the money from the sale to recover the amount we let you borrow." This agreement is called a mortgage.

Well, what if the property loses value after the loan is given? There's a risk to the bank that if the property is later worth less than the amount originally borrowed, then the bank could still lose some money because the property won't sell for as much as was lent to buy it. So, a way to ensure against the potential risk of a loss in property value is to place a cap on the amount of money the bank will let you borrow compared to the value of the property that you're buying.

Banks typically set this cap around 80-85% LTV, meaning that a bank will only let you borrow up to 80-85% of the value of the property. For example, if the property you want to buy is valued at $100,000, then the bank will only let you borrow $80,000 from them. That way, if you stop making payments and the property decreases in value, the property would have to drop in value from $100,000 to less than $80,000 before the bank would lose money on the investment.

So if the property costs $100,000 and the bank will allow you to borrow 80% ($80,000), where does the remaining 20% ($20,000) come from? It traditionally has come from the borrower (the homebuyer). That's where the "conventional 20% down payment" concept came from.