My initial logic for a random pack in game, was the excitement of running home and seeing which surprise launch game would be yours. Then you can talk to your friends about it...and possibly if you know several people with the system you can all play and try different launch games and possibly increase sells of each launch game.
The problem is I want to play Mario Kart, so I purchase the Switch and Mario Kart, I run home to realize Mario Kart was my free game. OOPS. Now Nintendo could easily make it that if you register a purchased game you would get a different free game. Or if you purchased the free game you were offered you could pick or get another random free game. But that complicates the system and could be confusing. Something like this you would want to be simple and understandable.
I do think a "super" or AAA launch title is important for a pack in. Look at successful console launches and you see that they all had a great AAA title packed in. Or later they were released with a AAA pack in a year later. The pack-in game gives instant value to an expensive purchase. I can not say I would spend $249.99 for the chance to spend $49.99 for a game. Yeah I am buying an entertainment system which allows me access to buy more games. But to me, there is no visible value. You spent money for the option to spend more money.
On the other hand, the pack in game whether you want the game or not, gives you value. Yeah, I don't really care for Wii Sports, but its nice to have it. I am sure I will play with my friends, and the system now has even more value, because I can instantly play a game.
A multiplayer Pack in Game also motivates the buyer to consider spending more money on an additional controller or accessory. Local gaming is brilliant on getting that second controller purchase and getting more revenue for the system.