The sudden transition from mouthpiece to neck has more than once drawn attention. It looks odd, indeed, the wideness of the mouthpiece chamber meeting the narrow entrance of the neck.
It is reported that some saxophonists have experimented with removing this transition by narrowing the inner size of the mouthpiece chamber to the size of the neck. Correct intonation then becomes impossible: the volume of the mouthpiece chamber is needed dearly. The Selmer company, among others, equipped its later models with an inner rounding-out at the entrance of the neck, although this is still a rather small one.
The German Fritz Seiffarth, about whom we know very little apart from that he submitted the German patent nr 593340 in december 1932, must have thought similarly, but more radically. In his patent he makes quite an interesting proposal. Seiffarth describes a mouthpiece and neck without any inner ridges or edges. He claims
'das Instrument einen vollen, weichen Ton erhält, also ein Tonveredlung erzielt wird [...] und daß das Instrument wesentlich leichter als mit einem normalen Mundstück anzublasen ist.'
As can be seen in the drawing, the construction is fairly complex and excludes the use of any other than a matching pair of mouthpiece and neck. This certainly must have been part of the reason for the construction to not be viable.
When I reinvented this construction around 1995 (certainly I should have payed a visit to the patents library earlier!) I could in retrospect confirm Seiffarth's claims. However, the same can be achieved in an acoustically slightly less perfect way which has the advantage that now conventional mouthpieces can be used.
This is what I did. Besides tapering off the rim of the neck itself, I slanted the entire entrance to the neck. This creates a more fluent volume transition between the mouthpiece chamber and the neck. In order to be effective the oblique part does have to have a certain length. For an alto, say, a centimetre and a half.