To run the 32-bit flashplayer natively, because your browser and all it's pluigns have to have the same number of bits, so to speak.
Yes, I know about nspluginwrapper. Yes, it works OK, but it has it's own quirks, and it takes slow to a whole new level.
So, there's 3 choices, 32-bit firefox with 32-bit flashplayer, 64-bit firefox with nspluginwrapped 32-bit flashplayer, and 64-bit firefox with 64-bit flashplayer. The first isn't an option for me without a reinstall, the second sucks, and the third also sucks, but, IMHO, sucks less.
So, to sum up a way-too-long answer; What's a convincing reason to use 64-bit flashplayer? Answer: Because or all the options for 64-bit Ubuntu, it sucks the least.