Why are plumed archers considered so good?

Title.

In castle age, plumes have 1 less range and 1 less damage than xbow. In imp, plumes maintain the 1 less damage but manage to get the range back.

Isn’t the appeal of ranged support units in their damage output, and losing out on damage output compared to the archer-line seems to be a very noticeable disadvantage to me.

Are the tankiness (something archers aren’t intended to be good at) and mobility (worse than the generic cavalry archer unit that you could use as an alternative if your goal is to play with mobile ranged units) really worth the lost damage output, especially given you can use eagles to provide mobility and you’re never going to outrun cavalry civs in any scenario anyway?