i believe you're trying to put your agenda into a place it doesn't belong and won't fit.
He is not saying the priests profane the sabbath by rejecting Him as Messiah or by adding tradition. He says they are blameless for what they do.
Why were they Blameless Post. Did the Levites create their own Priesthood? Did they give themselves the Service of the Priesthood and the duties thereof?
Or did the Holy God of Abraham give them duties "apart" from the Laws of the rest of the people?
He is drawing attention to the fact that priests doing what the Law commands them to do, profane the sabbath in the temple. He says you can read about it in the Law. the demands of the temple supersede the sabbath within the Law: and He is greater still than the temple.
No, you infect the scripture with your own religious tradition and bias against God's Laws. Jesus does no such thing. The Pharisees condemned Jesus for following the same God the Priests followed, only the Pharisees didn't condemn the Priests, yet condemned Jesus and the Disciples. Why did they do this? Because they were following God's Law? But God's Law exposed them as hypocrites for condemning their own Messiah, but not condemning the Levite Priests for doing the same things.
22 And Samuel said, Hath the LORD as great delight in burnt offerings and sacrifices, as in obeying the voice of the LORD? Behold, to obey
is better than sacrifice,
and to hearken than the fat of rams.
23 For rebellion is as the sin of witchcraft, and stubbornness is as iniquity and idolatry. Because thou hast rejected the word of the LORD, he hath also rejected thee from
being king.
they're accusing His disciples of profaning the sabbath ((verse 2)) - which He does not refute. instead He points out that in the Law, the erstwhile 'disciples' of the Law are required to profane the sabbath, and He is even greater.
He's telling them that their accusations are absurd, and that they should believe: if they understood mercy, they would not have falsely condemned His disciples, which He calls guiltless, just like the priests who in the Law are guiltless though they profane the command not to do work, or to kindle fire and cook.
He does refute. "But if ye had known what this meaneth, I will have mercy, and not sacrifice, ye would not have condemned the guiltless."
The Levite Priests, like Jesus and His Disciples, were following God's Commandments, not the Mainstream preachers doctrines created from the Commandments of men.
It was never against God's Law to walk in fellowship and eat a strawberry or ear of corn on His Sabbath. It was never against God's Commandment to help a brother in need on the Sabbath.
That is your Law, it was the Pharisees Law, it was never God's Law.
Jesus exposed their wickedness and their hypocrisy.
11 And he said unto them, What man shall there be among you, that shall have one sheep,
and if it fall into a pit on the sabbath day, will he not lay hold on it, and lift it out?
12 How much then is a man better than a sheep?
Wherefore it is lawful to do well on the sabbath days.