They allow me to see if I'm missing something (another way of looking at it they also prevent me from being totally unjust). So they are ok as an information source, but can create nasty incentives.

So you don't give them too much weight, you don't want them to influence employees too much. We used to do that and it impacted company culture negatively IMHO. Now it is under 20% of the score and so it cannot be abused, but it remains a useful tool.

I want to do 360s on the managers two level up and higher. Because they are the real problem in my view. I hate snitching on my direct team members not knowing how the the feedback is used so I usually just praise them without much detail.