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I can understand that when applying for a credit card that Citibank would want to review the application but I've applied to open a checking account with Citibank and I've been waiting 2 weeks for a reply....to open a checking account. I had no idea that it was such a decision as to whether they would accept money FROM me.

Perhaps they are having trouble verifying your identity?

Not weird. Banks love their overdraft fees, so they are a de facto lender to anyone who has a checking account. That makes you a potential credit risk.

Banks are increasingly careful about whom they do business with. More due diligence is being done these days.

But then again Citi offers an account with no overdraft fees called the Access Account, so it's not like you HAVE to overdraft your account anymore.

The only downside is the account doesn't come with checks or premium features.

Even in that case, a new customer still represents a risk to them. Handling bounced checks isn't free. Neither is fraud. (Not that OP would bounce a check or commit fraud, but the bank doesn't know him from Adam.)

This risk is the reason why companies like Chex exist - https://en.wikipedia.org/wiki/ChexSystems

It's also the reason why prepaid debit cards like (like all of the 'bird products) exist - a sizeable chunk of the U.S. is unbanked because Chex has a negative opinion of them.