I get a little cranky when I am on a website and it is such a difficult thing to find a way to communicate with that company. The larger the company, the worse it is it seems. Then, being able to communicate directly with a human is a challenge. These little irritations are not good for customer retention, which is far more important than customer satisfaction.
The websites that we build all have easy communication. The phone number is large and it is on every page. We usually have a contact page also, and it will have more information and probably have photos of the humans as well.
Communication is something I think you would want to encourage rather than discourage. Even a complaint can be a powerful opportunity to solidify a relationship. People don't necessarily expect perfection, what they expect is that you are interested in them and the issue they may have in front of them and be interested in solving it quickly and effectively. Doing that will solidify the relationship in a big way.
There is a blessing in every problem. One blessing is that the customer gets to see what your service is really like. The sales team can sell the customer on your service and paint a fantastic picture of how well you would be taken care of, but when the problem actually occurs, now is the time the customer gets to see if all that talk is true. If it is, the relationship is solidified. If it is not, the relationship is weakened--they lose confidence and they lose trust.
I know this from experience for sure, so based on this, why would you not want to talk to a customer and especially if they have a problem. What an opportunity it can be. Make communication an easy thing and how the contact information is placed on your website is very important.