A bad mask (eg a bandanna) means less virus gets out, but it is more likely to get out in the form of a fine aerosol that hangs in the air for hours. On the opposite end it is a reminder not to touch your face (prevents transmission from your hands) but won't stop you from breathing in an aerosol.
Likely still a net win, but kinda a hard thing to do good research on.
There is no doubt that masks that are designed to block things the size of viruses help. Just issues about who is the highest priority to get them when they are in short supply.
Do you have a reference for this? I've only ever heard of aerosolization primarily being a concern around people on breathing assistance equipment.
The root cause is offshoring safety critical manufacturing:
https://www.wired.com/story/decades-offshoring-led-mask-shor...
These are all "perfect is the enemy of good" fallacies, not "debate".
Also, how does a bad mask increase aerosol? That makes no sense.
Note in particular that cloth masks were tried and failed during the Spanish flu epidemic.
Given that I can't find it repeated, I suspect that it may be misinformation on my part.