The problem is that while you’re being frugal and saving, the house price keeps going up. The longer you save the more you have to save and the less affordable it becomes. If you buy sooner you get that appreciation.
That happened to me and my wife in the mid-1970s. We were trying to save enough to buy our first home, but inflation was raging during the Jimmy Carter regime. We couldn't afford homes we liked and needed to save more for a down payment. By the time we saved enough, the starter home we got was more expensive than the nicer homes we passed on just 6 months earlier. We did a lot of extensive work on that starter home to fix it up. Sold it ten years later and moved up to a nicer better home. We were smarter on the 2nd home, and got a loan from a friend in order to pay 20 percent down and avoid the insurance cost if we had only paid 10 percent down. You pay insurance against a bank loan if the down payment is less than 20 percent. Friend was happy, we paid that 2nd loan off within two years at 10 percent a year, we were still better off not having to pay that insurance cost against the primary loan. We paid extra into our monthly payments to bring down the principal, enabling us to pay off the loan within 15 years.