Yes, credit cards "cost more" on fraud issues and that's why they get different, higher interchange fees.

But in general it depends on the place - US has a strong legal difference between fraud on debit and credit cards, but there still is some fraud protection even for debit cards and in (for example) EU the consumer rights for debit cards also includes chargebacks for unauthorised transactions and compensation of losses with stolen/fraudulent credentials above a certain level (100 EUR if I recall correctly); and banks still require a lot of monitoring infrastructure and security people to reduce debit card fraud simply because customer satisfaction requires that the fraudsters don't run rampart.

Banks in the US don't really care about credit card fraud "that much" since the onus is on the merchant. Since debit cards require a PIN, the only fraud that even comes up is cloning and PIN scraping via fake ATMs (chips might help here, but they have these problems even in Europe, so I'm not certain).

Know more about EU set up but the reality is that there is a lot of infrastructure costs and some fraud as well (~4.04bsp @$101 average). So costs for ~$2000 in fees can be up to ~$400. Signature cards are not secure whereas EMV cards hit a 0.42bsp fraud rate ($148 average).

Of course still room for profit but the above numbers show why merchants are interested in EU fees and security.

It definitely does. It didn't use to be the case, but many banks now offer the same protection from credit theft as a credit card. My local bank only requires that I alert them as soon as I notice it, but their map-reduce jobs have always caught the crooks before I would have ever known.