This game seems like a more "Hardcore" take on the Thing-Thing series. The levels and objectives seem to be designed with the timer in mind, which makes for a more challenging and rewarding gameplay experience. If the timer were removed, then the level design and objectives would be pretty much useless.
Also, it's a good thing that the game doesn't save the objectives if you die. This makes it so that you try harder not to die, especially if you complete a lot of objectives, and helps improve your skill at dodging enemy attacks. I also like the enhanced customization. I love me some custom characters. And the music is pretty sweet too.
If the lose of objectives to dying, or the timer were removed, this would have been a much less rewarding game. It's challenging, sure, but it's that special kind of challenging where you can see where you messed up, learn from what you did wrong, and still have a great time playing, regardless of how difficult it is. It's kinda like an old NES game like Mega Man.
However, to be fair, being lenient towards a player might just be have its own rewards too. A difficulty option would have been nice. Overall, though this game did a fantastic job at, reusing old elements from the older games and adding in new levels and objectives that let the player feel rewarded for being good at the game, and even help the player get good in the first place.