I was on a 7 night Fantasy, so I can only speak for that.
There are a lot of characters scheduled. If we showed up 10 mins before schedule, we were 1st or 2nd in line. If we showed up at the scheduled time, we had a 5-10 min wait.
Right when we got on the ship, there were unscheduled characters on the balcony that the kids were able to walk right up to.
We only had crazy long lines for the princess gathering (skipped it) which is now ticketed.
For the Sea Ya Real Soon party, there were about 12-14 characters in the atrium with no photographers- it was take your own pics- and my girls literally got to walk up to almost all of them. There were maybe 2-3 people in front of us for all of them. We jumped from line to line and saw about 10 characters that I took pics of the kids with in about 10 mins.
My kids were constantly bumping into characters in the halls who would interact and visit with them- princesses would stop and talk to them and pose for a pic and many of them "knew" my kids by the end of the cruise, chip and dale would stop and dance with them and play ring around the rosie, pluto would stop and pretend to dig for bones with them. Rapunzel came up to us in the hall when my grumpy 4 year old had to leave dinner and we were walking to the kids club. She knelt down and talked to her and then took her hand and walked her to the kids club with me.
The clubs themselves also have plenty of activities with the characters. I would often pick up my kids and they'd be curled up in a princess's lap reading a story.
Also, wake up with Disney Jr and other dance activities in D Lounge and dance parties were very close encounters. The kids got to dance up close with Goofy and Jake and for some of the activities, there would only be 6 or 7 other kids there.
This was all for a September cruise.
We did not have Aurora on our ship, so we stood in line for her at the park after, and gosh, it was more waiting than almost all of our waits combined on the ship.
Also, Disney is super strategic and the main characters- Mickey, Minnie, et al have difference costumes for difference days/events.
DCL attire, tropical attire, CC attire, Pirate attire, formal attire... so even if we hit them up and got a photo, we had to get a photo for each "costume".