Changeable Default Firing Mode
There should be an option in the Options > Gameplay menu to change your default firing mode. The choices should be either the current in-game setting, or the mode you last selected.
Case in point: the Bar M1918A2 currently always defaults to the slow fire rate full auto mode. Since I like to play CQB, it's better for me to have this default to the faster fire rate full auto mode. Even when I have the bipod deployed, it's better to have the fast fire rate full auto mode on because the recoil gets reduced. If I'm standing (i.e. not using the bipod) and I'm shooting medium to long distance, then that's when I prefer to manually change the fire mode to the slower fire rate mode.
Overall, it should be set to the firing mode that you use most often, which the current in-game default does not always represent. So, this request is mostly a quality of life improvement.
This may be too late to implement for BF1, but I think it's a good idea to look at for BFV.
Just my 2 cents.
It already shows you the current fire mode.
You can see it on the bottom right where it says "V".