I agree with Patrick (not unusual) re: depth of swale.
There seem to be two flavors of Biarritz par 3's - both built by Macdonald and/or Raynor about the same time.
The "classic" Biarritz did not require a long carry to the front of the putting surface in those pre-watering system, small ball days as there was no hazard between tee box and green. Hence, 50+ yards of roll before the green was the norm. Examples include Piping Rock and The Links Golf Club (NLE). I'm sure there are others, but I have not played them. At Piping, the ground is no longer firm enough, and the ball is too big, to play that shot anymore - which has probably been the case since after WWII.
The other type of Biarritz DID (and still does) require significant carry in order to safely reach the front section of the green. Examples include The Creek, Fishers Island and, especially, Yale.
In fact, while Yale is the prototype Biarritz green, the hole was clearly designed for the aerial game even back then as the carry to the front of the green is 160+ yards from an elevated tee box. Other than for the most expert of shot makers (then and now), I don't see how playing the shot to the rear section of the green by running it through the swale with a low punch was, or is, the percentage play.
While Yale's Biarritz is usually considered the course's signature hole, I submit that the average golfer has always tried to carry the ball to the back section of that green via US Air.
Perhaps Pat Mucci has the skills to hit the low, 165 yard running punch shot. I know I don't and I don't know many club golfers that do. Also, is the green even kept firm and fast enough for that shot to work?
As an aside, Tillinghast made the par 4 13th green at Somerset Hills a legitimate Biarritz green, I think. The green isn't quite long enough, but the swale that runs the full width of the green is certainly deep enough.