We learn that “publishing” the fact of the purchases is to forestall claims of the goyim that Israel stole these lands.
Though still we might question: all of the Land of Israel is promised as a gift by the Creator of the World to the descendants of Abraham:
Genesis 12

and the descendants of Jacob:
Genesis 28
as well as being conquered by Joshua.
Then what is so special about these three places that they need added protection from future false claims?
This type of question was certainly raised theoretically by Torah scholars during 2,000 years of study during the Exile, though today any student following current news events can tell you: in the Holy Land, there are no other places where any Jewish presence is more controversial, and faces more international resistance, than Hebron, Shechem (Nablus), and Jerusalem (the Temple Mount).
A fast look at the map will show that all of these sites are located on the “Gav HaHar”, or mountain backbone/spinal cord of the Land of Israel, between East and West, and on the watershed line between the Jordan and the Mediterranean.
We can gain understanding from the explanation of a sage some 150 years ago. He writes that each of these 3 places is a symbol of one of the Foundations of the Children of Israel:
Shechem= Torah
for here we swore an oath to observe the Torah in the Land of Israel on the first day of our entry into the Land at the time of Joshua:
Deuteronomy 27

Hebron= Kingdom
for here David was crowned King over all of Israel:
II Samuel 5

Jerusalem= Holiness
for here is the fixed Gate of prayer for the entire world:
I Kings 8

And, of course, without Torah, Kingdom or Holiness--- the Children of Israel would be just as any other nation, for these are the tools with which the Jewish People help Manifest the Kingdom of G-d in this world!
So, we have learned from the Torah, the Midrash, the Words of our Sages... as well as from current events, that those evil forces who would try to drive the Children of Israel out of:
Hebron
Shechem
Jerusalem
know exactly what they are doing!
They are working relentlessly to destroy the Jewish Nation,
and to detach the Creator from His World!