Is it "fair" when Boss Monsters have a fixed initiative instead of rolling it?

I've recently bumped more and more into the "issue" that I rolled rather low on boss monster initiative which irks me in the flair of the encounter.
Sure they have legendary actions to bridge the gap but it still feels somewhat wrong to me when the largest threat moves last('ish) behind every player and every of his mobs just because I rolled low on the boss' initiative.

It's a general pet peeve of mine that there are lots of player abilities that increase or give advantage on initiative rolls while so far I haven't seen a single bestiary monster that has any special bonus to their initiative except for their dex score.

So I had the idea of doing it "Lair-Action style" and just give the Boss a flat initiative of 20.
How do you do it? Do you roll all the initiatives or do you also have some sort of system with static initiative? If yes, what are you experiences with it?