Is there any reason why you don't want to carry an expensive lens? Do you live in an area high risk for robbery? I am not mocking you but I don't understand the logic.
I bought the same lens for almost 2 grands. I use it as much as possible to get the money's worth.
If you are bothered by the weight, that's a different matter but you didn't complain about that.
You are spot on- it is the high risk of robbery especially for street photography. My 5Dc+40mm costs ~$ 500. Not cheap, but not something I will claim insurance for.
I am not particularly strong, but the 24-70 doesn't feel heavy. It is actually an extremely balanced lens. Nothing wrong with wanting to use it as much as possible. I
rarely never find a reason to keep it home other than security.
I bought the eos M because I want to hand over a cheap camera to strangers when I need to be in the picture. It proved to be a great idea after a recent vacation. People have no problem using it and were surprised by how fast the camera shoots. Yup, people who are used to p&s and phone camera have no idea the M can shoot so fast.
I think you should keep your 5d mk 3 and your standard lens in your bag. Then shoot with your M. When you see something you really like and you know you're safe, you use your 5d. That's what I'd do if I was in your situation.
I don't think getting a cheaper lens would solve any problem other than relieving GAS. As long as you have something big around your neck, it draws attention. If you use M, which you shady have anyway, you can keep it in your jacket or your pocket if you have baggy pants.
That's my honest opinion.