When are you flying? Many AT flights book up at the last minute - there are many people (like myself) that wait until 2-3 weeks prior to book flights. With AT's cheap fares right up to the 2-week prior point, they often fill up with last minute travellers. Getting 3 seats together will be next to impossible, even if the flight isn't full, because those that have paid for seats will want to surround themselves with empty seats, and may be more apt to choose the middle of a row of 3, know what I mean?
We've seen families split up on every AT (and Allegiant) flight we've taken. I've also seen the many, many posts on here of how people had a fit that their small children were split up because they didn't pay for seat assignments, and no one was willing to move (as they had paid for seats, they should not have to move, and will not be made to move by flight attendants). If your kids are willing & able to sit alone, then by all means, skip the seat assignments, but just be prepared that they most likely will not be seated together.