The reasons for testing Y-SNPs depends on your goals. There are two broad categories of researchers that should be interested in researching Y-SNPs: 1) deep ancestry researchers and 2) genealogical researchers. These two kinds of researchers have very different objectives but also mutually benefit from each others research. Behind the scenes from most genealogist's view, deep ancestry researchers are working away diligently discovering new Y-SNPs and adding new branches to the haplotree. Behind the scenes from most deep ancestry researcher's view, surname project admins and many active genetic genealogical researchers are working away building clusters of related lines that provide the vast majority of the data that deep ancestry researchers require for their analysis. As Y-SNPs approach the genealogical time frame, deep ancestry researchers lose interest in these less broad "private" Y-SNPs. On the other hand, genealogists are more interested as these less broad "private" Y-SNPs could have major genealogical implications.
For deep ancestral researchers, their primary goal is discover and document very broad branches on the deep ancestry descendancy chart of mankind. The discovery of broad Y-SNPs have the largest impact on the maximum number of researchers. Discovering more recent Y-SNPs gives deep ancestry researchers the ability to analyze global migration patterns of our ancient ancestors. Many of these researchers are also interested in clan based studies and are attempting to determine how clans are connected and evolved in the distant past. In the last year, many Y-SNPs are now approaching and entering the genealogical time frame. In this time frame, many deep ancestry researchers become less interested in these "private" SNPs since their breadth is limited and only have genealogical implications. Unfortunately, the deep ancestry decendancy chart of mankind stops just prior to entering the genealogical time frame and these Y-SNPs are called "terminal" Y-SNPs.
For genealogical researchers, discovering ancient deep ancestry branches have minimal impact on genealogical research. When these Y-SNPs are over 3,000 years old, the primary usage by genealogists is that these branches can be used separate groupings of submissions into smaller groups. After all, if your ancestor does not share common ancestors 3,000 years ago, then they obviously can not share ancestors in the 300 to 600 year time frame where most genealogical research is being done. Another major usage of these earlier Y-SNPs is determining the rarity of DNA haplotypes. If few mutations are found between the ancient MRCA haplotype and your surname cluster MRCA haplotype, you have very common DNA values where close genetic matches may not be related. Many surname admins and genetic genealogical researchers are not aware of this troublesome characteristic of "overlapping haplotypes."
Once Y-SNPs approach the 1,500 year time frame, these more recent Y-SNPs are much more important to genealogists and few genetic genealogists are aware of the power of the DNA fingerprint. If you compare the MRCA haplotype of your more recent haplogroup to the MRCA haplotype of your surname cluster, you can discover the off-modal mutations between the two MRCA haplotypes. These DNA fingerprints are a much more reliable gauge of relatedness than the number of mutations between submissions alone. For those Y-SNPs that originate in the genealogical time frame, these Y-SNPs are even more important as these recent Y-SNPs can define new branches within the genealogical surname clusters. Unlike Y-STR clusters where clusters can overlap and are not well behaved, Y-SNPs usually provide very well defined branches. In addition to well defined branches, Y-SNPs also provide information on how the branches are connected and the relative time frame of each branch. Although there are only a few dozen of these "private" SNPs today, new "private" SNPs are discovered at a very high rate and several new "private" Y-SNPs are discovered every week.
The deep ancestry research employs four very different DNA tests: 1) Y-STR tests where very ancient deep ancestry can be estimated but not at very recent time frames; 2) "deep clade" tests (a generic broad Y-SNP test for those starting out that reveals well-established deep ancestral branches that submissions descend from); 3) individual special order Y-SNP tests where more recently discovered Y-SNPs and "private" SNPs can be tested; 4) "Walk Through the Y" test which is a partial Y chromosome scan from FTDNA that discovers new Y-SNP mutations (other Y-SNPs are datamined from scientific sources similar to WTY testing).