Unless I'm mistaken, it doesn't say anywhere in the article that there will only be three live shows. It only says that each coach will have three artists when they get to the live shows (so 12 in the live shows).
If it works like the previous US one did, all twelve finalists (from the four teams) will perform in the first live show. Two people leave each week, regardless of which team they're on. This would give 5 live shows, assuming that 4 people make the final.
I could be wrong, but this seems a lot more feasible to me.