I have not found this to be the case. Bear in mind that when I make a story "Pay What You Want" on Itch, it is because it is being released for free elsewhere, including on my personal website and on platforms that do not permit monetisation (or mentioning that your work is monetised, which is an irritation) where I am much more popular than I am on Itch. I do not depend on or particularly care about discoverability through Itch itself outside sitewide sale events, I just use it as a sales backend because it's one of the few platforms that can and will facilitate the business model and permit the content of my work. A fair few customers per my analytics don't even open the Itch platform at all to buy my work, they do so directly via the widgets on my website. So generally a customer is coming in from a context where they understand well enough that if they pay for a minimum price work of mine, it is to get the opportunity to read it ahead of everybody else, and if they choose to pay for an otherwise free work that has rotated out of the premium window it is to financially support me out of a charitable impulse in a way that indicates support for (and potentially request for more of the kind of) that work specifically.
Generally they do not pay at all for PWYW stories because they're old and can be more easily read elsewhere for free in a preferred context. I only even turn the stories PWYW when they rotate out because it strikes me as silly to have the same product available in two different places alternately for free and for an obligatory price point, but I don't want to deny people the chance to donate to a work they genuinely love, which has happened a couple of times.
I might do this differently if I were interested in building a following on Itch itself, but since what I'm making isn't games I don't care about this at all.