You can be the cheapest logo designer on the internet and attract a lot of clients with this strategy. Of course it can work, at least up to a certain point. Because tomorrow, someone else will be cheaper. What would you do then, charge less?
A smarter way to go about it would be to charge what you’re worth and be “more” to your clients. More preferable to the next designer because you listen, you understand, you put yourself in their shoes, your designs are your best work. Your clients are comfortable working with you and enjoy the design process.
And they will come back to you with another project. They will also tell their friends about you. Not because of something they can measure like a dollar amount but for something intangible but has a greater impact.