No, you only have so much time to find a house, so you pick one quickly. Everybody I know that bought another home did it exactly that way, including my sister who moved just last year. There was no way she was going to speculate when she would be able to sell her old house and go bankrupt. After she sold it, the realtor wrote in a 60 day moving time which is pretty standard in the industry.
The person that wanted the house before the last buyer couldn't get the loan from the bank. That's why you don't buy a new house first. It took him over a month until the final refusal. Now if she waited all that time, then had to re-list the old house to start all over again, she would have been foreclosed on because most people can't pay on two mortgages.
So, your sister did not even look around and have some houses in mind for when she sold her old house, she just sold it and then started to replace it?
That is fucking stupid. What if the house she found after looking for a month had a 60 day moving time? Then she is homeless for a month.
I do not know anyone, ever, outside of those in the military being sent to a new station that sold a house without somewhere to live already picked out.
When you apply for a loan, they take your old house into consideration. Trust me, it's the way most people buy another home.
So you find a home for let's say 200K. To secure the loan, you need at least 20K cash to do it. Then the underwriters get the application, and deny or accept the application based on your income and ability to pay. You are denied the new home loan because you have an existing mortgage you are paying on. You are paying the mortgage, taxes, insurance, everything figured in. Even if you got the loan, it's likely at a higher interest rate than you'd get with a large down payment. And, you'd be broke paying on two loans instead of one.
Doing it the way most people do it, you sell the home first, buy another one, and use the equity plus whatever other money you have available to make the down payment. You get a lower payment, likely a little lower interest rate, guaranteed approval, and you know where you stand for your move to the new house.