But once you convert your coins to fiat, you need to deposit the resulting fiat in your bank account. I am not sure how much it is going to cost, but I suspect that it is much more expensive than the exchange fees and on top of that this process can take a few weeks to complete.
Then that is a problem with the fiat banking system. If you are paying fees to deposit fiat in your accounts, then you'll also be paying those fees when depositing fiat customers have paid you with.
Why should I care as long as I'm not made to pay for it?
Because your initial point was "bitcoin is too expensive". Bitcoin is actually far cheaper for merchants to use than credit cards. If more people understood this, then it could help adoption.
Let's hope Bitcoin will make them process these transactions faster
Yeah, it probably will. There is a new system being set up in the EU, which currently covers around 50% of fiat payment service providers, to process transactions instantly.
It is not merchants who have the say in these matters. It is buyers. So if buyers want to pay with credit cards (or otherwise), merchants will readily pay these excessive fees to Visa and its likes.
It goes both ways. If credit card companies suddenly put their processing fees up to 10%, you can bet merchants would either stop using them, or make prices more expensive for using credit cards, regardless of what the customer wanted. I do agree that merchants are unlikely to start accepting bitcoin out of the blue, because they need to know there is a demand for it, which is why I encourage everyone to approach any small or independent retailers you frequent and talk to them about accepting bitcoin. I've had a fair amount of success doing this.