I am a manager, but when I was an IC, I held your view. I learned that giving even softened feedback resulted in being at best ignored for a week, at worst, becoming a marked man.
I resolved to change this for my team. Ask for feedback broadly, and about projects, not me per say. Peoples end up commenting on the project/ sprint, and they feel safer. Much of what they talk about however, I have power over, so I view it as a comment on me and my execution.
Second thing, never once have I reacted negatively to negative feedback. Not in a team meeting, not in a 1:1.
Third, my boss has 1:1s with all my reports monthly. If I stop accepting negative feedback, my boss will hear about soon enough. I wish every manager had this hanging over their head. As an IC, all my code was reviewed. Managers need to have their performance reviewed frequently as well, not just bi-annually.
The one thing about my method is you have to be careful not to let the team become so free with criticism they just start ranting all the time and increase negativity where it isn’t warranted.