Which we do, every year, at Easter. I see no reason NOT to celebrate His Birth, because he had to be born, in order to die, so while his Death Redeemed us, His birth made that possible.
So where is it recorded anywhere in scripture where Jesus commemorated His birth, or where the Apostles or First Century Church ever commemorated it if celebrating His birth is so important?
The ONLY event that Jesus celebrated and admonished His disciples to commemorate each year, was His death. His birth gives us absolutely NO SALVATION from the penalty of sin which is death.
Only His blood sacrifice - His death - is of primary importance for commemorating according to the Gospels and the Letters of the Apostles.
And while you may see no reason not to celebrate His birthday - there is a scripture to keep in mind when one decides to reason things of God for themselves apart from the bible:
There is a way that seems right to a man, But its end is the way of death. - Proverbs 14:12 & Proverbs 16:25