The company I'm building right now has something similar to this as a major component of the service (feedback via text [SMS->email for the moment, but I'm also going to have it be visible in a web dashboard] ] is one of two methods I'm going to launch with.) I'm billing it as a "universal customer testimonial" service with a some added benefits. One of those benefits works like this: a business receives a message sent in via text. In order for the message to be posted publicly, the business has to approve it, but even if the business chooses not to post a message, they can read it and act on it (I include a message with each approval request that says 'If you do not wish to approve this testimonial, you may ignore this message. However, we do recommend taking even negative feedback into consideration in order to improve the product or service you provide.') So they get customer feedback, and can then choose to turn that into a public testimonial, or they can not post it publicly but still act on it.
Another benefit is a 'remind to review elsewhere' message. If the business approves the message, we send a reminder to review the business or product on a service of the business' choice (like Yelp, Amazon, etc.)
I'm hoping that the extremely low barrier to use (sending a text), will mean that these businesses get more feedback (since there are plenty of people who don't want to post on services they have to register for; don't feel like downloading an app; who wouldn't mind giving some feedback, but don't want to feel the pressure of 'crafting' a reply the way you often do on some services; who, even if they are registered, may just put it off forever because it seems like too much work, etc.) and so will have more information with which to improve their businesses. The idea is based on the 'praise publicly, criticize privately' maxim.