Markets will exist eternally if you define all human activity as market relations. What some European observers of primitive societies saw as barter was in fact gift relations (the difference being with barter you fix the relative values before exchange, with gifts you simply have to return a similar or greater worth at some point, or perhaps never, after all, an unreturned gift is a win at potlacthing).
Among the Hadza in Tanzania, they have been observed to have what some anthropologists describe as tolerated scrounging: if you are seen with some meat or honey, say, someone can walk up to you, and say "I want some" and you just hand it over, no exchange.
Among arctic peoples name sharing exists, whereby you get a cut of the meat based on your name (and in other societies it's by clan). In some societies, IIRC Polynesian, a man will not work his own property. His field belongs to his uncle, his scythe to his cousin, the cart to his nephew, etc. of course his cousin, uncle and nephew are working his land at the same time.
Andean peoples did engage in barter (as barter) but that was at quite a developed stage.
Extended gift relations may persist into socialism, even maybe the odd bit of barter, but this would be hugely marginal compared to production for use and concrete needs.
Of course, in all these types of societies, these relations are negotiated, but unless you define all negotiation as market (and thus all human interaction) they are not markets.
Market is just place where exchange of goods and services in the way something for something happens. And as far as I know nobody of great ideologist promised marketless economy.
However, market today is received as almost religious figure. For bourgeois press markets are an oracle that should be followed. For hardcore neoliberals like so-called an-cap bunch, free market is deity able to solve anything. But when it is showed to them that it can't exits due to own definition, they react as devout priest for blasphemy. For average communist, a market then must be a devil. And suggestion that it will never cease to exist is very painful conclusion. Denial of this fact is the most like reaction.
There is a lack of cold analysis instead of almost religious approach.
"Property is theft."
Pierre-Joseph Proudhon
"the system of wage labor is a system of slavery"
Karl Heinrich Marx