You have a chance at character Omegas in the challenges, daily activities, several events have them as rewards, and you can purchase them with fleet tokens or crystals on a regular basis. So I don't agree you get more ship omegas than character omegas in a week.
Plus a character omega ability takes 5 omegas to max out unless it has a zeta ability. To max out a ship ability it takes about 20 omegas I believe. I think all ships have at least 3 abilities so it would essentially take you about 5 weeks to max out a ship.