The oath of allegiance does mean a lot. Not denying that. In fact prior to 1986, new citizens at their naturalisation ceremony handed their green cards and foreign passports. My wife's father naturalised in 1977 and he needed to hand in his Pakistani passport then. In 1986, the US Supreme Court ruled that the United States has no right to determine if a person is a citizen of country X or not. Only country X has that right. So the oath of allegiance is still part of the naturalisation process, but it holds no relevance as far as stripping a newly naturalised citizen of his/her previous citizenship unless and until that country ceases to consider the new US citizen as theirs.
All US citizens need to enter and leave the US on their US passports, including those that hold another citizenship(s). I totally agree with that stance and abide by it 100%. However once outside the US a dual citizen is free to pick the passport he/she wants to use. There may be times when that person has no choice. Pakistan will let Pakistanis enter using a foreign passport. However there are countries (Albania, Iran, etc) that will not grant entry to dual citizens until they use their national passport. So what will someone do then? By your stance of not having the freedom to pick a passport, what will this person do?
I hope you understand the point I am trying to make.