it's a bit hard to tell since the doorways are not drawn so I'm judging by the arrows.
My main take from this layout is that the combat would happen in the flanks and not at the point where it would matter the most. I believe this since the flanks seem to be much more wide/open and therefore invite more players to fight. Also, the team holding the point might have an easy time to shut down the enemy team's fastest route to the point, forcing the enemy team to flank. The lower and upper flanks seem very long to me, and might be left sort of unused (except for the sneakiest players.)
You might want to make a koth map where the point is not the most interesting area (such as harvest) but splitting the teams into three areas (two large flank areas and also the point area) might make the combat too "thin" and less engaging. I suggest making the general layout more of a rectangle first, as flanks are always very long in a square map. Then I would try to emphasize the mid area somehow, for instance, by enlarging it.
EDIT: the number of paths seem fine btw