Disclaimer: I'm not a writer, but I do write music.

I think there are two types "bad" writing and I think people have a hard time having nuanced discussion about this.

First category is what I would personally describe "uninspired". These are works created by artists who arguably have either (1) too little exposure to prior art, or (2) too inexperienced with core skills of writing. So, in terms of my field, these artists probably (1) didn't expose themselves to enough music, or read enough music, or (2) didn't practice how to construct and write music enough times that they're comfortable. Examples of "uninspired" works include student works (i.e. practice works written by people to gain skills), works whose only purpose is to make money and there is no other consideration (this is probably very debatable), or works created by people who are unreasonably unexposed to the prior art (e.g. someone who has sufficient writing skills who is writing a novel, but really only read 2 novels before.)

Second "bad" category is what I would describe writing that is too stylish where aesthetic choices aren't appealing. This is when creator (1) is sufficiently exposed to prior art and (2) is experienced enough to produce works similar to prior art. Now, this gets very tricky because the problem with these works -- i.e. what separates them from Category 1 -- is that the work itself needs to convince the observer of these qualities, which can oftentimes be very hard. Unfortunately, I cannot give examples from literature, but to give an example from the history of music writing: oftentimes people listen to works of Schoenberg and they complain it sounds horrific, dissonant, random and ugly etc etc... However, if you look at the work closely, you'll find choices that are only consistent with thorough understanding of the prior art and an experimental desire to create something entirely novel. Now, it is "ugly" (for some, of course) but it is well-informed. In other words, it convinces most that the artist was able to create something "prettier" but for whatever reason decided not to.

Unpacking this is important when consuming "bad art" because each category teaches you something else.

When you consume Category 1 "bad art" you need to pick up (1) in what ways this work is unaware of prior art, and (2) in what ways this creator is inexperienced. This can be crucial to understand points where you struggle. E.g. you look at some student works, and you see consistent patterns that diverge from prior art -- consistent patterns are not explained with creativity. This can be a good reminder to work on these skills.

When it comes to Category 2, it's more complicated. This kind of art can be jarring, but can be the most useful kind of art you can consume to perfect your skills. These can show prior experiments, and how various styles work. You don't have to enjoy it, but it will be useful to see. E.g. slow movies may not be your favorite, but if you're filmmaker you likely want to sit through the entire "2001" movie.

Ultimately, it's up to you, and up to your relationship with your art. I personally consume a lot of art I dislike and think it's important to expand my understanding how things work. An artist is not just the work, but also the entire lifetime spent on observing, and critically thinking about other humans' art. So, the answer ultimately lies in you.