"It makes no sense."
That's a good point. The rules aren't explained in-game. Players will probably become confused when they clear a single, double, or triple and the game abruptly ends. The pre-game screen should say something like "How many Tetrises in a row can you make? Clearing anything but a Tetris will end the game!" The end-game prompt also needs to be rewritten.
I suggested this because I believe players will find it more interesting, and it'll have more lasting appeal. Don't get me wrong, 50 Tetrises in a row is extremely difficult. However, given a particularly finite amount of time and effort, many players are capable of it. That means eventually the leaderboard will be filled with maxed-out 50 Tetris runs. In the end, it comes down to who can do 50 the fastest. Speed is interesting in its own right, but if I want to compete in speed, I can already do that in every other mode. The new rule rewards players who can make the smartest stacking decisions.
You may encounter piece droughts, but this still comes up even with the old rule. Perhaps a modified randomizer is in order (after x pieces, the drought will always end). Skimming is indeed an interesting skill that the new rule no longer rewards. However, skimming is already rewarded in many other modes. I think the pros of the new rule (needing extremely good fundamentals of how to put pieces together to maintain field stability) outweigh the cons of no longer rewarding skimming. Lastly, I believe, even with the rule change, Mr. Clewetts would still understand the reference and think the game is interesting.