Granted, this advice was a lot easier to consume when interest rates were at record lows...
You can just refinance out of it (when the numbers are right), and it’s often easy since you now have equity, a proven payment history, and are presumably looking at even lower payments on the new loan.
The mortgage company that we chose had a program where they did all of the underwriting before we even started making offers, and part of our offer was a certificate entitling the seller to $5000 at the mortgage company's expense if we couldn't get financing. Kind of like extra earnest money from the mortgage company offered as a guarantee that there wouldn't be any problems in closing.
We ended up getting the first house we made an offer on in spite of an insane market, so I guess it worked!
And even if you found a condo (usually 2x as expensive as a co-op for same QoL) without a board to reject you or just lived in a city without co-ops holding a lot of housing stock, banks have similar requirements in co-op applications as well. So you really need to have a massive income to go in without a >20% down.
Among the young people who may like to buy a house, this probably applies to a few rare folks working for a bay area tech company salary but are allowed to live in any other city where the home prices are more affordable.
It's been a little while since I've done this–I, at least temporarily, gave up the idea of buying something in the city–but I noticed similar trends to keerthiko. Similar to when I was actually looking at places with a broker.
I don't think I found a condo under 800k, while there are plenty of co-ops across the boroughs, including Manhattan, in the 300-800k range.
EDIT: just noted you said "in another place". In my experience it's very hard to find this information in America outside NYC without investigating individual buildings.
[0]: https://streeteasy.com/for-sale/nyc/price:300000-800000
Super interesting: "Today, there are over 1,100 HDFC coops that make up a significant part of the fabric of New York City's affordable housing stock. " https://www.nyc.gov/site/hpd/services-and-information/hdfc.p...
"5,578 NYC Co-ops and Apartments for Sale" https://streeteasy.com/coops/nyc
Though many of these might be from giant projects, it's still interesting. https://en.wikipedia.org/wiki/Mitchell%E2%80%93Lama_Housing_...
This is what you can do if you don't delegate all the management of the housing market to the Fed.
The mortgage insurance isn't nothing, but it's not a big enough cost to warrant waiting until you have 20% down if that's still a long way off. You can also very easily remove the mortgage insurance once you get to 20% equity, so it's not like it sticks around throughout the entire mortgage if you can't scrape enough together at the beginning.