One way to try to answer this is to look at the benefits of the WTO. The main two are Most Favored Nation and National Treatment:
Most Favored Nation basically says that if you lower a trade barrier for one nation you have to do the same for the others.
National Treatment basically means that you can't discriminate between locally produced goods and foreign goods. I'm not privy with the details but I'd spitball this is related to not favoring local businesses in government contracts, or at least not in broad daylight.
Conversely, if you were to leave the WTO, it would mean that your existing trading partners can now:
Lower trade barriers with other WTO members without lowering them for you; and increase trade barriers on you.
Favor their own local producers, and those of other WTO members, in lieu of yours.
(This of course goes both ways.)
A third benefit that you'd lose is the well oiled dispute resolution mechanism. (Edit: or as you point out in a comment, what used to be a well oiled mechanism.) Going forward you'd need to go negotiate arbitration clauses and put language to that effect in each trade treaty. Which I would imagine is not a big deal in practice. It would probably carry less predictable outcomes, but at the same time it could end up benefitting you on average if you're the 800 pound gorilla in the room.
A fourth benefit might also be that WTO members don't seem to go to war with one another very often. (They do impose sanctions on each other from time to time, though -- e.g. Russia.)
As to what the practical downsides and economic damage would be for any country that leaves, it would depend on the country and how much it trades internationally. Economists generally agree the WTO increases trade, so one might imagine trade falling when a country leaves, but by how much is frankly anyone's guess.