It is a myth that people don't take surveys.
The truth is that people don't take stupid surveys.
People are usually willing--sometimes delighted--to provide honest feedback about how you're doing and ways to improve.
But most surveys are not that. More often, the survey communicates in many different ways that the company (a) doesn't really care that much, (b) isn't interested in hearing the customer's honest feedback, and (c) won't change anything because of what the customer said.
Case in point: last night we had this voicemail left on our company's switchboard (click the link for the audio file). I have no idea who is calling or what the purpose of this survey is supposed to be, but clearly very few people are going to start answering random questions from a robocall which can't even be bothered to identify itself. The fact that most robocalls are highly scammy (and this "survey" is probably not legit either) should lead any company to think very hard about what this survey technique will do to their brand image. Yet we continue to see outbound IVR surveys.
On the other hand, our experience proves that when you ask customers personally for feedback (that is, with a person), give them the opportunity to say what's on their mind, and respect their time and opinions, in most cases the majority of customers will agree to take the survey.
So if people aren't taking your survey, it's not because people don't take surveys. It's because they don't take your survey.