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It's not 399 chances but more like 9 chances
Yeah, I keep making this mistake because in Poland many people play that the only way to get to 3nt is to use puppet which is ridiculous, I sometimes forget that there is middle way.
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And even if you were so worried about giving extra chances for them to double that you decided never to bid puppet on a hand where you would not have used Stayman, puppet would still gain on a fair number of hands.
But it loses space so you can't put all the 5-4 hands in there and you have less space for slam exploration.
All in all the difference is probably small if you don't bid puppet automatically on hands which should be bid by 2nt - 3nt.