I think there are two primary reasons for 3rd set TBs.
The first is in some areas, matches are played at facilities that have fixed court times, some as short as 75 minutes but 90 minutes is common. If you are lucky you have 2 hours. In all of these cases, a 3rd set TB increases the chances the match can be completed and you can avoid conflict with the following court reservation or having to deal with scheduling a time to complete the match, or worse, having timed-matches that require strange rules for determining the winner including resorting to sudden death points.
The other is that USTA League is dealing with a wide array of players with different abilities and fitness, and it is likely that for some (many?) playing a full 3rd set is considered too taxing. So this format increases the number of players who can compete without running into fitness issues.
I personally dislike 3rd set TBs and think fitness should be a part of it and a full 3 sets is not unreasonable, but do understand the points above, particularly the first.
Note that I believe that sections/districts/areas have the option for their regulations to say to play a 3rd set, or have it be an option the players/captains can agree to, but TennisLink requires the 3rd set be entered as 1-0 or 0-1 so there is no easy way to know if a full 3rd set was played.