Although that is the opinion of far too many clarinet players, the problem actually lies with the relaxed embouchure used on the hybrid horns. Although the mouthpiece used on a saxophone resembles that of the clarinet, the control of the clarinet reed by the lips and jaw requires a significantly different arrangement of pressure, tension and seal than does that of the saxophone.
Starting out with a relatively slack set of musculature and mastering the saxophone does not give you a good platform from which to start blowing on a clarinet. The rigid "smile" that you see on classical clarinetists is really a carefully arranged and balanced way of restricting the reed's vibration to the limited range needed for the classic clarinet tone.
To be fair, many clarinet players have some trouble adjusting to the saxophone's embouchure as well. However, for those trained first to the clarinet, it's a matter of slacking off, not tightening up. For most, using less tension rather than more is a much easier proposition.
I have problems when I have to make the jump from baritone (with a great big, loosely controlled slab of a reed) to the clarinet. Or, horror of horrors, to the tiny little Eb soprano clarinet, as I have had to do during runs of the 1970s show Company, where you go from a big, blasting R&B-ish dance number (with not one but two baritone saxes pumping away - it gave the bassoon player something to do) directly to a very exposed sequence of Eb clarinet solos in "Poor Baby".
(The solos are made more demanding by starting high in the instrument's range, then descending through a series of intervals down to the lower end of the horn. I have heard the solos taken on the soprano saxophone (there is a cued part for the Bb clarinet, for those clarinet players fortunate enough not to have been introduced to the Eb instrument, so transposition skills are not necessary), but, truth be told, the result lacks a certain "charm" afforded by the tiny little Eb instrument. No, really - it really does...)
Sondheim (or his arranger) even had the gaul to put a horn change in the middle of the tune, where you switch from Eb clarinet back to baritone for thirty bars or so of very subdued background tones, and then right back to Eb for a final, drawn out take on the solo's theme.
(At least the arranger saw fit to allow an extended phrase of silence in which to sit and contemplate what you were going to have to accomplish at the end of the tune - I always sat through that period with a sense of dread, fearing that my poor, over-worked lip was going to think it was still playing baritone when I made the entry in the upper register.)
It is at times like those that I wished you could manually adjust your embouchure with an arrangement of screws and knobs. But, it ain't gonna happen - you have to make it work with what God or evolution gave you.
And, there are some practitioners of the clarinet (Aker Bilk and Ted Lewis come to mind here) who have gotten by with a very loose variation on the clarinet embouchure. That method has had its adherents in the past, but they have always been on the outside of the clarinet world looking in. If you watch (rather than listen) to folks like Pete Fountain play, you will note variations in their facial posture at times as they "bend" the notes. But, their variations are based upon the basic clarinet posture in the first place, not as the foundation of their embouchure.
And, while you are dealing with the differences, remember it could be a lot worse. You could be having to switch from oboe to saxophone. I've always taken this as the reason for the invention of the rothphone...