I think it would be helpful to be able to filter the list of available matches based on whether the analysis option is enabled or disabled.
Also, in the games graph, it would be nice if matches with analysis were represented with an appropriate symbol (for example, a capital A inside the squared dot).
How would that be helpful? Just curious 
I personally don’t like playing game if analysis is enabled but I can only discover this after clicking the Accept button.
I also don’t like playing game if it’s enabled! That would be an interesting concept.
Please don’t use any analysis tool in live games. Only exception is for planning conditional moves in correspondence game.
Believe me it is very bad habit. It is some kind of allowed cheating. But you are cheating yourself. You become dependent on such tools.