Even if every Williams and Thornton does this - instead of thinking they'd rather have the NHL money, or are chasing milestones, or don't want to uproot their lives to go to a new continent, or don't think they can do a full season - we're talking 5-10 guys a season most of the time, most of whom are bottom six guys who go on to put up low playoff numbers. Signing them rather than throwing in rental mostly saves about a 4th.
Not to mention they're pretty much all min wage, so if a team believes in them enough to handshake at the start of a season, why not just sign them?
So no, I don't think it's the rule. The list of reasons NHL players don't go and wait in Europe for the post-season is long enough without waivers.
Again, you are going with the assumption that players would act the same if the rule was not there, which I don't believe would be the case.
Teams also have injuries throughout the season, so it's easy to come at the TDL with an active roster under 23 and a few IR player. Then you sign a few player at TDL and voila, you are over 23 players when the TDL is done and the roster limit disappear.