It does skew (at least the visual representation of) the data. However, it skews it in a way that is consistent: if you compare the shape of the line or an individual normalized value across two normalized samples, you're still able to visually distinguish which sample is more enriched and by how much. Trace elements are much more variable across rocks than are major elements, so this is a powerful tool to visualize those trends and differences.
Normalizing to chondrite is essentially asking: how does this rock's composition compare to bulk Earth? Is it evolved (i.e., is it enriched in incompatible elements)? If so, how much?
Same idea for normalizing to depleted mantle, except now you're examining whether a magma is likely to have been derived from a 'typical' source (the upper/depleted mantle is the easiest/most common area that mantle-derived magmas are generated) or if you're dealing with a deeper or enriched source (lower undepleted mantle/metasomatized part of the mantle).
Basically, it provides two major things: the ability to compare between samples, but also to obtain information about your samples' compositions relative to important compositional benchmarks.