This was experienced already at an early stage of online banking - back in the 80s and early 90s in Finland - before the Internet version. What occured was extraordinary jumps in customer satisfaction and when we looked into them it coincided with taking e-banking into use.

Props to banks. By placing the findings of this survey in the context of a few recently released reports (World Retail Banking Report 2011 and Deutsche Bank Social Media Report), it appears that their channel strategy is working: 

1. Customers say online banking is one of the two most important channels for them (branch being the other). This survey finds customer satisfaction to be high on online banking.
2. Banks have a long way to go to catch up on mobile, but since their customers don't accord high importance to this channel, banks can take their time to set the right priorities for their mobile strategy. With time, they might find Mobile RDC to be the first mobile payments killer app!  
3. Customers say they're not too interested in connecting with their FIs over social media. Therefore, budget-starved banks can afford to hold on to their social media plans until customer preferences change. For now, as a representative customer, I'd be more than happy if banks replied to my letters / emails within a reasonable time - realtime tweets and Facebook updates are entirely optional!

However, there seems to be room for improvement in the branch channel. I hope banks do something about this instead of shutting down their branches en masse!

Customers pay every cent of the costs banks have - and it is especially expensive and not very sensemaking to have too many big branches designed for transaction services in countries where online banking has taken off.

I'm not so sure how many customers really believe that every penny they save for the bank comes back to them - I for one don't. According to WRBR-2011 report, it's in a country like USA where online banking is quite mature that customers find the branch to be the most important channel. So, I don't believe that cost or channel capability matter so much to customers while judging their banks' multichannel offerings. 

What does matter - and this is what banks need to keep in mind while allocating their multichannel dollars - is customers' perception that "the branch and internet (have) different strengths". According to the report, customers all over the world believe "The internet excels in information gathering, transacting, and looking up account status ... The branch is the preferred channel for solving problems, indicating the value of having a human touch in certain situations." 

I am saying that customers pay every cent of any service providers cost - not that they are getting back every saved cent. But for sure if cents are not saved there is nothing to give back. Our experience in Finland - where the combined costs of banks were cut in half - much due to branch closures enabled by e-banking - was that most of the costs saving went back to customers in fierce price competition. The other potential direction - the shareholders - got a much smaller slice.

Branches are important as sales offices - but we should by now try harder to get away from manual transactions of all sorts - especially cheques and cash.

@Bo H: With heavy competition in banking, banks have to sell as much as other industries do. "Branch as a sales office" is an innovative concept. Banks can shift as many transactions to e-channels as they like. As long as such shifts are aligned with the preference of a majority of their customers - rather than based upon internal costs or perceived channel capability - they won't face any risk of customer dissatisfaction.   

Starting to use onlinebanking is usually leading to a jump in customer satisfaction - and lower costs for the bank - and thus for customers taken together if competition is working. This does not mean that e-banking should not be charged for - but less than the manual alternatives.