I never succeed in thickening sauces with pasta water. What am I doing wrong?

You seem to have the wrong expectations. No, it will never be as thickening as a cornstarch slurry. If that's the level of thickening you expect, you are really better off using the slurry.

Don't forget that pasta water thickening is a traditional technique from the time when people did not go to the supermarket to buy a pack of cornstarch. They cooked down ripe tomatoes for several hours, and the starchy water saved from needing a few more hours of evaporation. Also, they cooked with homemade pasta, which had some flour residue sticking to it, not the perfectly-gelatinized industrial pastas we buy today.

If this is not how you cook, and if you prefer pudding-thick sauces, then the slurry is probably the better method for you.

I notice Kenji from Serious Eats has also tested pasta water and recommends it for flavor reasons. He also tested it for thickening - but against salted water, not against a slurry. That's what people mean by "it thickens" - it thickens when compared to random liquids, not when compared to thickeners.

There is also another thing that might have been meant in connection with "pasta water for thickening sauce". It is actually a very specific kind of sauce: an emulsion between pasta water and a liquid fat. There, you start with the pasta water, cook it down sufficiently, and stir in the fat into the hot pasta water. It produces a "thick" sauce - not as thick as, say, mayonnaise, but it is certainly thicker than the oil you are putting in, or than the pasta water itself. It may have been in this context that you have been hearing of "pasta-water-thickened sauce" and thought it meant that pasta water is a thickener for random styles of sauce.

Think of your pasta water as a tool for emulsification, rather than "thickening." Adding pasta water to your condiment pan has the benefit of helping the condiment form an emulsified sauce that adheres to your pasta. Add it a little at a time and swirl the pan vigorously. It also allows you to control how "wet" you want your final result to be without having to create other liquid components. Also consider that praises of starchy water generally come from restaurant cooks who are cooking many servings of pasta in the same water. Dry or fresh, as the evening wears on, that water gets pretty starchy, thus dramatically increasing its viscosity. We just don't cook that way at home.

As moscafj said, pasta water cannot be understood as a thickening agent at all. In fact, I understand it as a thinning agent: after your sauce has boiled down to more of a paste (great taste, but not very immersive to the pasta), you'll need some way to make it proper liquid again. What you do not want at that point is to make it runny, watery, hence adding pure water is problematic. Likewise with wine / juices / vinegar etc.: these can make a lot of sense for deglazing at the beginning of the cooking, but adding them at the end will make the sauce watery and also add too much of a raw, unsavoury note. And such pure hydrophilic liquids often don't completely merge with a hearty sauce with considerable fat content, making for an unappetizing phase separation: the water will tend to “wash off” the flavourful parts from the pasta on the plate.

Hence the pasta water: it liquefies the sauce, but at the same time improves contingency due to the starch content. Stock or cream can perform a similar role, but are less neutral. Depends on the kind of sauce what you want. Since you always have the pasta water, that is the first candidate.

All answers given here look right, and the folks that answered your question demonstrated they know what they are talking about. But there is a trick that was not mentioned: in case you have a proper pan and are cooking a short pasta (e.g., fusili or penne), you can use the sauce to cook the pasta. It is a different approach, but it is delicious - and the sauce will become thicker naturally. Give it a try!