We are speaking about very ranges to whom range 1 to 75 belong (as an exemple). From the point you know the pubkey of one of those puzzles, triggered by the send transaction,
you still have some seconds or perhaps minutes to highjack it and get the coins into your own wallet. In this process there are used bots running 24 hours a day, so that if such transaction
is detected they will start a programm to find the private key from the public key of that low range puzzle. Nowadays there are very fast applications powered by GPUs, not knowing if they use BSGS, Kangaroo or other methodes. Please notice, that this is only possible with small ranges, otherwise yes, this would endanger the whole BTC universe.