I wasn't aiming for an argument or anything, I just wanted to know what you were wanting. Check out some of the sweet VS matches online in youtube... They have some seriously good JP matches - search for "panel de pon vs". You won't however find many time trial matches (I found 1). It takes more skill to balance offense and defense, which is the real difference between it and time trial. I would definitely suggest playing VS and trying to get over that obstacle to improve upon your game.
Tetris Attack is still a confirmed tournament (like last year), and will be judged via VS mode. But that shouldn't stop you from finding any challengers for 2p time trial.