Your right, TP is in the similar situation no doubt so comparison is correct thinking. That said TP was off by 1.5mil, which is alot sure but still close.
Switch doesnt need to be as high as wii. It could still do 50mil and reach 10mil combined with LoZ wiiu. Look at the high sales some games got on wiiu despite a 15mil userbase.
That said BotW is tracking ahead of TP and ibwouldnt be surprised if it is already close to 4mil by end of its first month (shipped+digital)
It may be tracking ahead of TP, but at the same time PS4 was tracking higher than PS2 for a while. It's the nature of the industry that things today start off faster. Also, Breath of the Wild has the advantage of being the only worthwhile title on the Switch right now, which is why it has basically 100% attach rate. When Mario Kart 8 Deluxe comes out, we'll see less people getting Zelda with their Switch.
I believe that first month sales of the Switch were 2.4 million, so I'm not sure how BOTW gets to 4 million. It's not selling 2 million on Wii U in a month.
Zelda sold through 1.8mil First Month in Japan/US for wiiu/switch. Game is doing well everywhere else, so sell through at minimum is another 700k (that is Europe, rest of NoA/World). That would be about 2.5mil+ sold. There are a ton of copies in the wild (pun nintended). So yes i believe we have somewhere between 3.6mil-4.2mil shipped+digital.
As of BotW selling faster, i think itll leg out well. Time to tell, it wont do under 6mil. Thats all i kno. Ill go with my prediction of 10mil. If it doesnt itll still be close imo