Syndicalism tends towards fascism, not freedom. 1930's Italy, German and the U.S. were all broadly syndicalist. Two of them ended up with fascist dictatorships and the third came close (see John T Flynn "As We Go Marching" for a detailed account).
Yours is a gross oversimplification at best. You are ignoring, among other things, that in the 1930s the biggest and more relevant trade-union in Europe was the
Confederacion General del Trabajo (CNT), with more than 1.000.000 affiliates in the mid-1930s, and together with the
FAI it was precisely the forefront against the fascist counter-revolution. The CNT-FAI was able to control a territory (Aragón and part of Catalonia) for 8 years and installed an anarchist society which did not tend toward fascism at all, until it was crushed precisely by the army of Francisco Franco together with the help of the Russian
KPSS.
Furthermore, Italy was not "broadly syndicalist" and thus "it tended to fascism". Trade-unions had a minor relevance in Italy in the first 20 years of the Century, and when fascism raised strongly as an opposition to the Russian revolution of 1917 its first actions consisted in beating up precisely trade-unions members. Trade-unions gradually lost any relevance until 1923, when Mussolini established a single, vertical trade-union that made "unnecessary" those founded by the workers themselves. The fascist trade-union in Italy was a joke as it didn't represent the workers but the fascist party itself, and it was a totally vertical organization, which as you might understand is completely opposed to the anarchists organizations which are always horizontal.
Finally, it should be added the huge impact that trade-unionism had in UK, Scandinavia or Australia (just to name a few territories), which never gravitaded towards fascism.
As for the impossibility of a modern technological society without markets, prices and private property, see Mises on the Economic Calculation Argument (never refuted).
While all anarchists are against private property, not all of them are against markets and prices: Proudhon's idea of a working economy in an anarchist society was
mutualism, in which free market is a fundamental piece. In any case and besides Mises theories, the hard cold fact is that anarchism was tested empyrically only once (Aragón 1930-1938), and it was a successful experience. It should be noted nevertheless that the duration of such community was short lived (only 8 years) and its size was relatively small (less than 100k individuals living in it).
On the contrary, I'd say that the type of society the "an-caps" are looking for has been thoroughly tested in the past: the middle ages, with their lack of states or nations but the presence of private property (established by force, as usual), seems a good test-case for the "anarcho-capitalist" society. In fact, Rothbardian's like to point out how prosperous
Medieval Iceland was, and they consider it as an example of the ideal society. I would add that while Medieval Iceland was quite peaceful for middle ages standards, it remains the fact that it was a hugely unbalanced society were the majority of poor had to work for the minority of rich, and where justice or safety was available only to those able to pay for it (a minority).
There is a chance that free-markets offer the best conditions for the largest number of people.
