Hey Martin,
You are absolutely correct, the vocal tract must shorten or be made smaller in order to resonate higher harmonics. However, the fact is the larynx is only one part of the vocal tract and is actually very inefficient for high harmonics. One very strong resonance strategy is to maintain a stable larynx (or slightly lowering) in order to break its relationship with the second harmonic (H2). The singer can then tune or adjust the second formant F2 (by adjustments to the tongue, lips, etc.) to amplify the third, fourth or fifth harmonic (H3,4,5) depending on the vowel. This is a resonance strategy used by Pavarotti that Steven Fraser outlines so well here (half-way down the page). Note that Pavarotti does not employ a strong singer's formant but rather tunes F2 to H3.
http://www.themodernvocalist.com/profiles/blogs/vocal-ring-and-operatic-tenor
No, by "H" I mean harmonics. The singer's formant would be F3, F4 and F5.
In my experience higher notes are not necessarily harder with a stable larynx and a raised larynx is not always necessary nor desirable.