Why do many DNA solutions contain additional compounds?
DNA in pure water.
The only time that nucleic acids would encounter pure water would be in a laboratory setting--for example after an oligonucleotide is synthesized in vitro, the protecting groups are removed from the reactive atoms in the finished sequence and the final product is cleaved from the supporting matrix.  At that point you can lyophilize (freeze dry) the ammonium hydroxide solution, and resuspend the single-stranded oligo in pure water.
Additional compounds enhance heavy oligomer solubility.
However, as noted in the comments, nucleic acid solubility, particularly high molecular weight DNA, like genomic DNA,  is enhanced in solutions with dilute monovalent cations. 10 mM TrisHCl, pH 8.0, 1 mM EDTA suffices for almost every application. The EDTA inhibits any errant DNAses, and also slightly inhibits microbial growth.
Compounds act as pH buffers.
Tris is not the best biological buffer but has high solubility and is relatively cheap and stable. If the solution becomes too basic the DNA strands will melt, and if the solution becomes too acidic the purines will start to deaminate.
DNA never experiences pure water in biology.
From the moment that DNA is synthesized in a cell until that cell dies and its DNA is ultimately degraded, it does not encounter a pure water environment.