In fact, we can blame the delegates at the Constitutional Convention (as well as the 7th Congress) for that particular offence against Democracy. Back in 1800, The Constitution Article II Section 1 included "But in chusing the President, the Votes shall be taken by States, the Representation from each State having one Vote;"
The one state one vote rule does appear in the 12th Amendment, but it was already in the original Constitution.
A more important point is that this is only relevant if there is a 269-269 tie in the electoral college. The 12th amendment also says " The person having the greatest number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed;" Notice "Electors appointed" not "More than the number of states plus half the number of representatives" or currently more than 269.
It is (still in spite of everything) inconceivable that the race be called before it was agreed who won the tipping point state, but if it is decided that a President elect must be declared while the winner of some state is contested, the matter will not go to the House voting one state one vote (as always results must be certified by the House voting the normal way one representative one vote).
It has not always been true that all states are represented in the electoral college. It hasn't always been true in my lifetime (I was born on November 9 1960 the day after electors were elected November 8 1960 but before those electors Kennedy). In 1960 the electors for Hawaii were never assigned because the outcome was contested when the electors voted. This means that Hawaii had to wait until 1964 to be represented in the electoral college after becoming a state on August 21, 1959.
