If Joseph and Imhotep were the same person, this would mean that chariots existed in Egypt as early as the third dynasty.
In the third dynasty, only high officials like the pharaoh and his chancellor / sage / vizier were afforded a chariot to travel in.
Chariots in the 3rd dynasty were not horse drawn, they were carried by a procession of servants.The Hebrew word (merkabah) in the Bible can be translated as ‘chariot’ or ‘riding seat’. It does not distinguish between a vehicle that is horse drawn or a vehicle that is carried.
The enigma of chariots in the third dynasty is, therefore, easily explained.
Horse drawn chariots were used for military purposes and were not introduced until the 12th dynasty. Most of the chariots of the 12 & 13th dynasty were lost in the Red Sea at the time of the Exodus and paintings depicting horse drawn chariots in the 12th dynasty would not have survived.
It is hardly surprising then that there are no findings of horse draw chariots before the 15th dynasty unless, of course, one accepts that the chariot wheels found in the Red Sea by Wyatt in 1978 were from the 12th and 13th dynasty.