Should the sun appear very low in the horizon if its path is always between the two tropics? If the sun never rises above the tropic of cancer and never goes bellow (southern) of the tropic of capricorn then it seems that it should appear to the observer lower and lower in the horizon for as we move north. But from what I have seen this is not what I have observed traveling in northern and southern countries.
Am I not remembering right or is my expectation wrong?
Your explanation is correct, so you are not remembering correctly. The farther north you go, the lower the sun is to the horizon at noon.

Of course it depends on how far north you go. If you only travel 5° farther north in latitude, then the sun is only 5° lower in the sky. 5° is a "long" ways to travel on the earth, but in the sky 5° lower is not that noticeable.