Based on the erotic manga by Emily.

Will there ever be a major anime studio backlash against fan subtitling (fansubbing) of anime?

Most studios do commissioned work for the big publishers or other bigger studios, so it doesn't affect them a whole lot.
But anime property owners/right holders, whether a big publisher or the actual studio, still make most of their money domestically, with character licensing and merchandising being the cash cow. It's not so much the anime itself as it is the "property" and it's value in a licensing and merchandising sense that is important. Anime broadcast on TV in Japan, for example, are made almost entirely for the purpose of pimping merchandise and making the property attractive to licensors, which is why anime is made so cheaply.
(Budgets for anime, even full length movies, are shockingly low compared to animation in America, for example) The people who get hurt by fansubbing are the foreign licensors.
From the end of the 90's until the mid-2000's when anime was big on American TV, Japanese licensees demanded large minimum cash guarantees (called MGs) up front from licensors, and they bore little to no risk.
However, even in those "good old days" of foreign licensing, it still didn't really make Japan a lot of money relative to overall revenues for the property, which comes from the domestic market. As others here have pointed out, simulcasting and such are happening to beat the fansubbers, but for Japan I think fake merchandise in Asia is a bigger concern.
Piracy is a concern too, but not fansubs.
I'm not saying they don't care, but it's not priority right now. I'm no expert on the subject, but I used to work in animation in Japan and that's what I observed.