Why should an altar be made with uncut stone?

Even though allegorical methods are criticized they should not be excised from the conversation.

Acceptable worship of God is done God's way. The stone is the way God created it. It requires no work of the hands of men to be acceptable to Him.

An idol is a creation of man where he worships his own effort. We might paraphrase the words of Nebuchadnezzar "Isn't this great [whatever] that I have built..." just before he started eating grass. [1]

The imagery of the sword as the word says that the Word of God should not be used to make an idol of God's altar, as Satan perverted the word to tempt Jesus in the wilderness. He was hacking at Christ (the Stone) with the sword/word in order to destroy the altar of God and engender worship of himself.

Recognizing the stone as the Word of God expressing the law/Holiness, having intact stones is the equivalent of "not a jot or tittle" being lost before the law is fulfilled.

   [1] Da 4:30 The king spake, and said, Is not this great Babylon, that I have built for the house of the kingdom by the might of my power, and for the honour of my majesty?