In what ways could this situation fail?

It can work out. We did something similar a couple of years ago; the only difference was our mortgage was already paid off. We looked for a new home at the same time we were selling our existing one. You can set the sell date to whatever is needed (within limits, the new purchasers do have input in this).
To be fair, ours did not work out exactly so you need a backup plan, a place to stay in the interim. We could not find a home we wanted in the price range we wanted prior to our house selling and refused to just settle on any old place. We allowed our daughter to house us for a couple of months while still searching.
It all worked out. We bought the new one with the proceeds from the old, no mortgage so we were happy.

Find the house you want, and put a subject on it,
Example: selling the house you have now, the only problem if someone comes along and wants that house while your waiting for yours to sell,and they have the funds right now, they have to give you something like 72hours to make your offer liquid,if you can’t the other people get the house you want.
You can also put off the possession date of when the new owners get your house, but most people want possession as soon as the funds are in place.
Being mortgage free in this day and age is very smart, one of you loses a job or gets cut back you can weather it a lot easier with no debt,good luck and all the best.

You can do it if you sell the house before you buy a new one. I fyou sell the old house first you will have enough cash to renat for a month or two. Paying cash for a house you can get a 15 day close of escrow, so it would not be a long time.

One consideration is the tax consequences of that much profit. A married couple can shelter $500,000 in capital gains; beyond that it is taxable.

@rojo When you say we can set the sell date, do you mean we let the buyers know we won’t be moving until we find a new home type of thing?

@ItalianPrincess1217 Yes, basically. As I tried to indicate, there is some flexibility and it can be negotiated. When we sold our the buyers wanted to stay where they were for about three months. They had a rental lease and wanted to wait until that expired so they did not have doubled payments. Of course, we were amenable since it gave us more time.
You will for certain have to have some sort of deadline. I don’t think you can say they can’t have it until you buy one. Although, you can buy contingent upon selling your home. Again, if both parties agree.

Many sellers won’t accept a contingency clause so it is unlikely you would be able to negotiate a buy with that. Also, most buyers will want a closing date within a reasonable amount of time after getting a mortgage commitment. Your best bet is to sell first and if you haven’t found a house you want to buy at the same time (or don’t know when you will sell) decide where you can rent for a short time while looking. Paying outright for the new house will make you attractive to sellers but you do want to look into tax implications as @zenvelo says.

There is also something called a bridge loan which is not a mortgage but a short term loan that you might be able to take out between buying and selling.

You can put a “contingency” on the contract for the house you want to buy that says you need to sell your house first before actually buying the new one. When markets are very strong, and the housing market is pretty good right now in most of the country, sellers typically won’t do a contract with a contingency like that, but you can certainly try.

Read the contract well, and make sure you are ok with the parameters of the contingency.

You can sell your house first, and then quickly try to find a place. Maybe even rent for a short time, but that’s moving twice, unless maybe you can stay with relatives for a few months inbetwen.

If I were you, I’d spend a day looking at houses and be sure you’ll really like something in your new price range. Just know it could be emotionally difficult out, because if you see something you love, it sounds like you probably can’t buy it just yet.

Downsizing significantly usually is much harder than it sounds. Will you have to get rid of furniture? Give up a play room? Possibly, you can downsize, but you won’t be in the situation of no mortgage, but a smaller mortgage? Lots of possibilities.

I’ve had no mortgage a couple of times and it’s great. If you can manage it, it might be great for you too. You can save what you have been paying monthly, and your saving will grow quickly.

Remember that closing on a house costs some money.