As far as I know, contracts for kpop idol groups are usually that long. SM artists usually sign contracts that last about 7 years, but for example Exo's contract has a longer duration (rumored to be 10 years).5:00 for the bts rumour.
I feel like the contract they signed is kinda tricky and may be bighit is onto something. Because they signed the boys for 7 year' contract but after 2 years into the contract each one of them individually will have to go to millitary. In case bighit didn't plan sth for the rest of the members (like shows and giving interviews) I don't see the point in making that long contract. We all know bighit is greedy. They will not pay the boys if they don't profit from them enough. They will either not go to millitary or the company is planning other things to do with them, even when they are gone! What do you all think?
Regarding enlistment: I read on twitter, that enlistment time does not count into contract time. That would mean, that BTS has actually 9 years left with Bighit, since each member will spend 2 years in the military. However these are only twitter rumors. I haven't researched if that is true. If someone knows anything about that, please share, I would be very interested!
I think they are counting on the attachment the fans have, so when BTS returns they can pretty much pick up where they left.
Another reason could be that as long as they are under contract they HAVE to work for Bighit and no one else. Even if RM collaborates with someone as a solo artist or Suga writes a song for someone else, they have to ask permission. And I am sure that Bighit also get their cut of any profit they make of these collaborations. Suga seems to be quite respected as a producer, he made songs for other artists that were fairly well-received. Even after his service he could be quite successful. Bighit is not going to miss out on easy money like that.
In my opinion, they will definitely enlist to keep their image up. They are not as well-liked in Korea as you would expect. If they don't enlist they will be seen as unpatriotic traitors. I think the only way for them not to enlist and keep face would be
a) an exemption that basically orders them to stay out. In a way that everyone in the Korean public would think "Oh they wanted to enlist, but were forced not to. It wasn't their decision, there was nothing they could have done about that."
b) all found to be incapable of performing service. This is highly unlikely. Suga and Jin might have a shot a this, but not the others, as far as public information suggests.
Oh, and Bighit certainly has content planned to keep fans attached during that time. Maybe a new game? There are rumors that netmarble is working on another BTS game.