Whether you must garrison archers in towers depends on the situation and the type of Tower.
Watch Towers/Guard Towers/Keeps? Maybe
Bombard Towers? No
Is it viable to Garrison Archers in Watch Towers/Guard Towers/Keeps?
Do you need the extra range the tower can provide plus the ability to passively heal your possibly wounded archers? Then, yes. It can be okay to garrison archers for a tower rush too.
Also, you need to take into account the fact that some archers contribute much to garrison arrows… like the Chu Ko Nu.
If you need mobility, no.
Usually, it makes sense to garrison archers only in the campaigns as towers (at least the watch tower line) get obsolete by the Imperial age thanks to heavy siege and cavalry.
Is it viable to Garrison Archers in Bombard Towers?
During the Imperial Age, only Bombard Towers are viable.. for the most part. Trying to garrison archers in a Bombard Tower has no effect whatsoever with some exceptions.
10 hand cannoneers in a Teuton Bombard Tower makes the Bombard Tower fire two cannon balls, and garrisoning a similar number of Janissaries makes it fire three. Does this make a huge difference? Maybe to deal with Paladins and War Elephants but otherwise, no. It might have been pretty viable back in the days when Bombard Towers did hack (normal) damage rather than pierce damage as the effect could be devastating against rams but it has been over 18 years (as of today) since Bombard Towers were modified to do pierce damage for balance reasons.