As answers to Why don't we thank God for making us men/women? say, men thank Hashem for not making them a woman because the obligations or mitzvot that a man has is greater in number than that of a woman, slave, or non Jew.
However, why don't certain classifications of Jews (i.e. Kohanim or Leviim) make a declaration of their own highlighting the preponderance of mitzvot they have over regular Israelites?
Your question is referred to in the review Beis Hillel כסלו תשס''ה under the title “Why does not a kohen make a blessing שעשני כהן".
Rav Asher Anshil Schwarz asked the question and offered several answers. Relevant to your question is:
From the Mogein Shaul
He also cannot make the blessing “שלא עשני ישראל ” because a kohen is included in the designation ישראל. Further, he would be glorifying himself in the shame of his friend because until the sin of the golden calf, the temple service would have been in the hands of the Israelites.
