Do you have to honk to prevent a crash so often that the 2$ would add up to anything? It's negligible compared to the cost of the car. You're still incentivized to honk as the cost of a crash is much higher than the cost of honking

Not me but remember that there are people who don't have as much money as we in IT do.

Another issue is that this is something you need to do in a fraction of a second or it might be too late - if the first thing you do isn't smashing the steering wheel but hesitation in the form of thinking about money, it's probably going to be too late.

I have to honk to prevent a crash about 2 times a week - and I go to and from work (30 km combined) and nothing much else. What about professional drivers?

Actually the concept is interesting. You could even make like: 30seconds free per day, or something like that.

I've found that the majority of honks are not for urgent situations

There are people who would then intentionally honk for 30 seconds a day so they could feel they'd had their entitlement.

I fear it would make things worse?