I certainly had a little chuckle when I finished typing "poop collection" haha.
I think for a snake type game like this, the grid based movement makes more sense. It helps make it very clear where you can and can't navigate. Which is important to be able to determine quickly, and at a glance, while you try to plan your next move, or several moves.
For me personally, if the game was more free movement, I would feel more inclined to be upset at the game, then my own skill, if I couldn't fit through a gap I tried to leave for myself. Especially if I was one pixel off, or made the gap one pixel too small. A one pixel difference can be really hard to see depending on resolution. While, yes technically, it's my fault as the player for misjudging the gap, or lack of skill for making the gap big enough, it would be too easy for it to come off as the game just feeling less responsive. Like I'm battling the physics of the game instead of playing the game (if that makes sense lol). Unless you spent time implementing some really nice forgiveness mechanics.
That's just my two cents on it. Maybe others would enjoy the extra challenge from having free movement. So, maybe free movement could be like, a "hard" mode or something? Lol