What Good Is Kolmogorov Complexity Since It Is Relative?
The relativity is up to an additive constant. Suppose that you express Kolmogorov complexity relative to your favourite universal Turing machine&nbsp;$U$, but I do it relative to my favourite UTM&nbsp;$V$. If the shortest program for&nbsp;$V$ that outputs a string&nbsp;$x$ is&nbsp;$M$, then the shortest program for your machine&nbsp;$U$ can't be any longer than the one that simulates&nbsp;$V$ running&nbsp;$M$, and that has length $|M|+k$, where $k$&nbsp;is the size of the simulator.

So, yes, you could pick a UTM that has a very efficient coding for some finite set of strings. However, that would increase the length of the coding of at least that the same number of other strings, and we're typically interested in the asymptotic behaviour of infinite families of strings, rather than individual strings.