Median string problem & multiple sequence alignment
Why is this approach not used? Are there any algorithms that use it?

As shown in this paper, the MEDIAN STRING problem is NP-Complete on alphabets of carnality greater than 3. While the problem isn't used directly in approaches due to the complexity, the idea of trying to create a consensus sequence between pairs of input and using that as building blocks is common. These are considered &quot;progressive alignment methods&quot;.