1. If somebody has experienced such complications with their banks already, it would be interesting to hear about their stories
Traditional banks usually don't like Bitcoin and in my country few of them have already tried to stop accepting money from exchanges or to exchanges accounts (like if the exchange was depositing money on my bank's account or if I was sending money to the exchange's bank account).
Then the exchange filled a suit against the bank(s) and one or few of them had to start accepting money from/to this exchange again. But the process took some time to finish and I'm not sure if it is the final justice's decision yet.
2. If more and more banks adapt similar measures (or even stricter ones, like some credit card companies disallowing financing of cryptos all together), what do you think the implications on the market place will be? For instance, do you think exchange without KYC's will suffer?
I believe without giving your personal informations to the local exchanges when converting the money to fiat you won't be able to deal with Crypto-Currency. While the money is on the internet in BTCs everything is fine, you can continue anonymous, but once it goes to real world the bureaucracy starts and there isn't much to do about it. The market won't suffer at all because there will be always gaps, mechanisms used by whales, big investors to avoid some bureaucracy. Exchanges might suffer a bit, but they can move their businesses to friendly countries, right?
Truly, the banks should suffer, because people can abandon their currently banks and search for new more interesting banks, that is possible to be done.
3. Do you think this could lead to "ICO heavens" where only ICO's will have a chance to survive that undergo a stringent background check that would be acceptable for banks?
If this happens Crypto-Currency will turn itself into the traditional financial system we have today.
In a doomsday scenario, I could even imagine banks globally to impose similar restrictions worldwide, and thus even killing the entire cryptomarket.
That is why national sovereignty is important, each country has it own rules (and if possible each part of the country), so we can have countries that are friendly or hostile to Crypto-Currencies, this way developers and enthusiasts can choose where to operate their businesses and in the end we will see on the practice what country's model works better.