On the headline question:
In a section titled “The Sea of Suf,” Elitzur writes about the Israelites’ crossing of the Red Sea after leaving Egypt. He takes issue with those who claim that the term “Red Sea” is a misspelling of the English translation of Yam Suf – “Reed Sea.” While most modern scholars identify its location as one of the two Bitter Lakes, which are today part of the Suez Canal, Elitzur writes that the entire Gulf of Suez, which encompasses the Red Sea, is the correct location of the “Sea of Suf,” as it is termed in the text.No one thinks that "Red Sea" is a misspelling of "Reed Sea." Red Sea comes from the Greek translation of the phrase yam suf in the Septuagint. The literal meaning of yam suf is "Reed Sea."
I don't know the latest on this question, but the Oxford Bible Atlas (mine is an old 1974 edition) suggests that in the Exodus story yam suf may have been "the southern extension of Lake Menzaleh" (p. 58) which is on the northern coast of Egypt. The "bitter lakes" are further south, north of the Gulf of Suez.
The OBA also says that in later biblical usage (e.g. 1 Kings 9:26) yam suf referred to the Gulf of Aqabah (the extension of the Red Sea on the other side of the Sinai).
Linguistically, writes Elitzur, the Hebrew word “suf” refers to the sedge or papyrus. This freshwater plant grows on the banks of the Nile and is also found on the shores of the Bitter Lakes and in the Northern Sinai Peninsula. By contrast, the Red Sea is a salty sea that does not have such vegetation. Nevertheless, he writes, “In every place where the information found in the Tanach is clear, the biblical Sea of Suf is the Red Sea. Etymological speculations in scientific reconstructions of miraculous events cannot simply brush away hard data.”The "Sea of Reeds" was the name of body of water where reeds didn't grow? Maybe. I would have to see the argument in greater detail.
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