I think all ICU nurses would prefer the most critical assignments, all the time. My unit has a new director and she actually just addressed this issue in an email last week. Apparently nurses were calling in before their shift and discussing possible assignments with the charge nurse. Our director put the smack down on that.
Also, the most critical patients on our unit are often CRRT, Arctic Sun, or IABP, which not all nurses are trained for. However more nurses are being trained in these modalities all the time, which the charge nurse making the assignments may not be aware of. Therefore, the same nurses were getting CRRT, etc. over and over. Our director instituted a formal rotation sheet so that all nurses get a chance to practice and keep their skills up to date.
It's probably not possible for anyone to make an adequate assessment of your situation based only on the information in your post, but I will share a few of my generic thoughts as a brand-new nurse.
Even though many patients may seem "stable" to us as ICU nurses, they are still critical care patients, requiring a higher level of monitoring and care. In fact, that is what the majority of the unit is made up of. My unit has 20 beds. On an average day, I would say probably 2-4 of those beds are acutely
unstable, decompensating, on pressors, going for emergent scans, etc. There may be more patients on the unit who are stable on pressors... but pressors do not make a patient automatically interesting for us in the ICU, lol. So when you think about it, there will be 10 nurses on the unit, and less than half of them have those really critical patients. But, that doesn't mean that you will be one of those nurses half of the time. Since continuity of care dictates most of our assignments, you might end up going weeks between "fun," exciting patients. It's just luck of the draw.
One thing to think about--who are you taking/giving report from/to? If it is mostly other newish nurses, then maybe you are truly being discriminated against. But, when you take & give report to more experienced nurses, there is no reason to think that assignments had anything to do with a "lack of trust."
Hope this makes you feel a little better. If not, I would recommend going straight to the source--ask your charge nurses and managers, "just out of curiousity," when you can start taking more critical assignments.