No doubt a huge feature if true, although just how much memory the 3DS has to support this idea is in question, although ever-reliable SD Card support is definitely there.
Doesn't the game basically come on an SD card? What would be the point of transferring it to another one? Oh, and SD cards do fail, yo! I'm sure the ROM ones the games actually come on are totally solid, but the RW ones that consumers use to back stuff up do magically erase themselves and start to become dodgy after enough writes and re-writes.
SD card usage aside, the installation thing is a good idea for a handheld. For the very few who actually use their portable games machines whilst out and about (rather than sat in their bedroom with their DS plugged into the wall), an installation so that they don't have to carry so much stuff around is great.
As for size, memory is cheap these days, and Nintendo like to overcharge their customers. 3DS will be at least £200, I'm sure it's not an issue for Nintendo to include 8GB internal memory designated for installs. That's four games right now, given that the current max for 3DS cards is 2GB.
Steam (as others have mentioned) would be one model of getting around the piracy thing. I've no idea how practical this is, but perhaps some form of hardlocking whereby one card is good for one installation at a time, only. If the user wishes to install to another system, they must first put the card into the system it was originally installed upon, and uninstall with the game inserted.
Game then knows somehow that the installation that was used has now been uninstalled, leaving the game back at square one, where it can be installed to another system. This is probably a bit truncated, and doesn't account for what would happen in the case of console damage/loss/theft.
One solution for broken consoles is that the installed games be sent to Nintendo with the console, and they unlock your games in the event that they need to give you a new 3DS, or the one you had went through such significant work that it rendered the installs useless.
Or, they could just include it with the hardlocking Graeme was talking about, and to hell with anyone who loses their 3DS or breaks it.
Or, this rumour is false.