Multiple samples per pixel and texture blurring As far as I know path tracers (or super-sampling antialiasing) typically calculate the final color of a single pixel by averaging the result of all samples taken inside that pixel. This gives a nice anti-aliasing effect on the edges, however has the side effect of slightly blurring textures, because they most certainly do not have enough samples for each pixel, so samples have to be guessed with some kind of filter (like bilinear). From a mathematical point of view, averaging those samples applies a box low-pass filter to the reconstructed texture. This causes blurring.

How do path traced renderers/SSAA usually deal with this blur? Is there no way around it?
In signal processing, it is well-understood that you cannot accurately reproduce an analog signal of higher frequency than half the frequency of your digital sampling rate. That's just how the math works. Various aspects of rendering are just forms of signal processing, so this applies here too.

So you're going to get some kind of artifact. You have a choice: aliasing or noise (aka: blur). You're always going to have some of these. Aliasing artifacts are usually very noticeable and considered quite distracting. Human vision tends to focus on motion, and aliasing artifacts almost always create motion where none existed (especially when animating). Human vision is generally much more tolerant of noise, as noise patterns don't appear to move nearly as much. Plus, our eyes have their own anti-aliasing filters that impart some noise to what we see, so we're somewhat used to it.

Broadly speaking, you deal with it by not dealing with it, because it's preferable to the alternative. Yes, you can reduce the effect of noise with better anti-aliasing mechanisms, but broadly speaking, you're still going to have noise.