If BTS members are puppets and have no rights/control wtv, then that's only YOUR assumption. Cause if it's true, then they would've released another song like Dynamite or Butter this year, a full 'proper' album and then go on tour before enlisting. The amount of revenue & profit they can generate in tour alone is MASSIVE.
BTS can literally sell 3M tickets this year alone if they WANT to tour and generate atleast 360,000,000 USD and that's not even including online concert tickets and merch which can rack up to 700,000,000 USD and MORE. HYBE literally has to sell ultra expensive album and pump up more merch per usual to atleast get the revenue that they could get in touring.
Now, I'm not saying that BTS is in full control of their career. They are still an employee under a company, but they have the LEVERAGE and POWER to negotiate or demand better terms for their career. Meaning, they clearly have a say.
BTS contract runs out until 2024 and by then HYBE needs to sign BTS. And for them to pursue the members, they have to agree to some terms that BTS wanted like a 'break' from group activities and no full-scale touring this year.
IDK what's goes on in their government and whatnot, but I believe that the guys also want to perform in front of fans even just for once. We can all assume about the government-hybe-bts affiliation, but we don't know what's going on behind the scenes AT ALL. After what happened this year and how vocal BTS has been in that festa video, I believe BTS members are grown adult and can handle their own business.