Are there many mandated "time outs" in tournament bridge?
The Laws of Duplicate Bridge indicate (in Law 73) that


  Calls and plays should be made without undue emphasis, mannerism or inflection, and without undue hesitation or haste. But the Regulating Authority may require mandatory pauses, as on the first round of the auction, or after a skip-bid warning or on the first trick.


The ACBL is a Regulating Authority that does require mandatory pauses for skip bids. The ACBL Codified Minutes, Chapter XII, Section A have this to say:


  A. How and When Made
  
  Players should protect their rights and the opponent's by announcing, prior to making an opening bid on the two level or higher, or prior to making any subsequent bid that skips one or more levels of bidding:
  
  
  When bidding orally by saying, "I am about to make a skip bid. Please Wait!"
  When using bidding boxes, by placing the stop card so the LHO sees it (the skip bidder is responsible for gaining LHO's attention). The skip bid is made. The stop card is replaced in the bidding box.
  


...


  C. Opponents of Skip Bidder
  
  
  All Players
  
  When RHO has announced a skip bid, the player following the skip bidder must wait for a suitable interval (about 10 seconds). In waiting the player's manner must be one that suggests he is an active participant in the auction (the hand should be studied during pause). any (sic) obvious display of disinterest is most improper.
  Experience Players
  
  Experienced players expected (sic) to maintain proper temp (sic) whether a skip bid is announced or not.
  


I've never seen a director called to protest that opponents are not using the stop card but would expect to see one called if an opponent was clearly using the stop card only for weak bids. I have seen director calls after a player took far longer than 10 seconds to make a call after a skip bid and his partner took a bid at his next turn.