The way I explain this requirements to my student is that the proof-of-work is just as important to me as the end result. It's like in math class: you don't just write the answer, you need to show your work. Your commit history is not distinct from the assignment, it is part of the assignment.

Regardless though, my students usually are at a point where they don't have a commit style. They come to my class with no knowledge of git or version control -- I have to teach it to them.

Secondly, labeling you a possible cheater doesn't condemn you to anything, it just puts you on a shortlist of assignments to examine more closely.

Thirdly, this style of committing has helped more than a few students out when their computers die mid assignment and they need to move to another computer. It also allow me to help them with their assignments. When they come to me for questions, the first thing I ask is "have you pushed everything to your repo?" Instead of trying to debug over a virtual desktop connection, I can run their code locally and get to the cause much quicker in my own environment. It really works out well for everyone involved.