This is certainly a legitimate concern. As Christians, our chief focus should be upon the improvement of our own souls, so that our example might inspire and encourage others to do likewise.
At the same time, I find it significant that the first words of the New Testament -- a full sixteen verses -- are devoted to a rigorous documentation of Joseph's descent from King David.
If God did not want us to ponder this subject, on some level, surely he would not have filled the Holy Scriptures with so many references to it.
I see what you are saying, but the genealogy given stopped with Christ. It was provided to validate his lineage.
If God wanted us to ponder genealogy beyond the birth of our Savior, He would have provided additional information.....