If the virus is in microdroplets in your breath, something in front of your face when you breathe out is going to slow some of those droplets down, making them less likely to be inhaled by others nearby. This is just physics. If it can fog your glasses its helping. If it makes you smell your own breath its helping.
A scarf is better than nothing, just like a homemade mask is better than a scarf, just like a purpose built mask is better than a homemade one.
Mitigating risk by using methods approaching zero efficacy is useless.
"This is just physics".
No this is just your intuition. Scarfs don't protect you or others. Neither do gaiters. This has been tested. They may work mildly for UV protection... But there you can be fooled as well.
They just don't work. N95s provide a level of protection but they are not full proof. The further away you move from N95 the more useless they get. Cotton etc. don't protect. They are overcome by physics.