Thursday is the only possible day, but it does suck. There simply must be a free day both before and after the quarterfinal game for every team. This wasn't always the case in the past, and it was extremely unfair for the teams that had to play back-to-back games, one of which was the crucial quarterfinal play-off game. It's always said, and rightly so, that winning or losing the quarterfinal game is the separation between success or failure in this tournament.
In order for the four quarterfinal games not to overlap, they'd need to be spread over two days, Wednesday and Thursday, which means Tuesday would need to be a free day for every team, and all group play would need to be completed by Monday. That's just not realistic if each team is to play 7 games in the round-robin group. That would be 7 games in 11 days – insane. As it is now, it's 7 games in 12 days, which is an extremely packed schedule, too, with several back-to-backs for each team. The only solution, I guess, would be to start the tournament one day earlier, on Thursday instead of Friday, but perhaps that's unrealistic.
And, it doesn't really make sense to spread out the 4 quarterfinal games over the whole of Thursday, given that it's a regular weekday and most fans wouldn't be able to watch anyway. The 4:15 pm start is tough enough.
On the whole, the current tournament model with the two large round-robin groups is a lot better than the previous nonsense with lots of 4-team and 6-team mini-groups in various tournament stages. That was confusing like hell, and mostly also unfair. Whereas now in the two large round-robin groups, the battle for the 4 play-off spots tends to be very exciting every year, right down to the final day or final minute of final group game. (The relegation battles are nice as well.)