Hmmm, bit of a mixed bag here, I feel! Some of the modes are pretty decent, but some of the other modes feel rather bad and actually contribute to giving a bad first impression, so I would nix them altogether, ideally, and just keep what works.
Classic mode is pretty much the worst of the bunch and contributes to the terrible first impression that I was talking about. Once you've seen one classic mode level, you've pretty much seen them all as there's really no way to significantly scale them up or diversify them in any meaningful way, and the levels reflect that by just changing up the green area size or adding pre-built boxes which is incredibly shallow (how the hell is a level with pre-placed boxes considered a new level? I could make that level by just playing the first level and putting the blocks in myself, and it's pointless anyway because I can just click the boxes away as if I placed them! Was that intentional, or a bug?) The levels in Classic mode aren't tests of skill or wits, they are just tests of patience as it is a foregone conclusion to eventually win by just filling everything in bit-by-bit.
Breakable mode is just Classic mode with a bit of time-pressure: it still suffers the same dilemma as Classic mode where every level is functionally the same and is therefore quite boring, but at least it has something to encourage the player to play quickly and therefore be a bit more engaged. It's a step up, but I would still consider this a mode that should probably be removed.
The Precise and Bad Pixels modes is where the game starts to have some decent ideas. I still don't think it's that fun necessarily, but at the very least there is actually some manner of skill and decision-making required from the player to reach a solution, and the levels actually start to diversify themselves in interesting ways, such as having multiple green zones with their own count requirements. It's here that the game actually has something slightly interesting to it, and I feel that these should be the only two modes the game has: better to showcase the best part of the game than risk the player getting bored from the other modes which are given top billing and could lead to them quitting before the good stuff. At the very most, you could maybe combine these two modes with the breakable rules as well to create the best of all worlds (though the breakable rules might be a bit annoying when having to manage everything else).
Oh, and I do like how you can click and drag to put down multiple blocks in a row: helps avoid flaring up my carpal tunnel from having to click every individual square, so thanks for that!