NOTE: The single note names I use in this article are note names for the lower register. Unless I specifically mention otherwise, the fingers also translate to the notes a 12th above.
There are two keys and a key mechanism that make life easier, but that you don't often see on Boehm system instruments.
The left Eb/G# key
The "articulated G#" mechanism
The "low Eb key
THE "LEFT Eb/G# KEY is what it says; a way to play Eb or G# using the left little finger.
This avoids some very nasty and perilous slides between C and Eb in the clarion register and F and G# in the lower register.
For example, in first movement of the Bruch duo for viola, clarinet, and orchestra, there are several instances when the player has to slide from clarion Eb to C. (You can't use the LH C key, then the RH Eb key in those passages because of the notes surrounding that interval.)
Fast or slow, this slide is always perilous, especially with silver plated keys, which are more "sticky" than other types of plating. In addition, the C key is usually placed ever so slightly higher than the Eb key, which may not be a problem for people with thick fingers, but for those of us with thin fingers, it's almost impossible to make the progression from the Eb to the C cleanly without adding a little blip between the notes.
This key makes life a lot easier in this and many other passages! All you gotta do is get used to it and know where it's advantages lie!
In non-Boehm systems, the "German", "Oehler", "Reform Boehm", or "simple" systems, many clarinets have rollers to help.
Only one maker that I'm aware of offers them as an option, Wurlitzer, which makes custom clarinets to order. I'm sure there are others.
Why aren't rollers offered on "normal" clarinets? I have no idea other than that people just don't want to get away from something they're already used to.
THE "ARTICULATED G#" MECHANISM provides a way to trill from Bb or B-natural to C# without having to alternate fingerings from the left hand to the right hand. All you do is finger the Bb or B-natural and press the C# key to get the C#; you don't have to pick up and put down any fingers on the right hand. For example, in the second act of Carmen, the Entr'acte solo on the Bb clarinet has an F#/G# trill which is a real stinker. The articulated G# makes it easy.
This also works for the notes RH ring notes below Bb-- A, Ab, and G---though some clarinets don't respond as well here as others.
The single drawback to this mechanism is that you can't use one of the nicest fingerings for the altissimo, the wonderful "long F". (Thumb, register key, six fingers, and the C# key.) However, in a pinch, you can use the throat Ab key to play a long F with the articulated G# mechanism (no C# key), though the tuning, at least on my clarinets, is sharp.
Also, If you don't like the idea of having to lose your long F or you're perverse enough that you like trying to coordinate you RH pinky and the fingers on your right hand for trillls and tremolos, several clarinet makers, most particularly Patricola, have designed the articulated G# mechanism so that it can be disabled.
THE "LOW Eb" KEY lets you play a half step lower than the lowest note on a "normal" clarinet and also lets you play a resonant Bb (not the stinky sound produced by the register key/A key Bb).
(Astute viewers might notice that the photo is of a bass clarinet, but the keywork is the same on soprano instruments.)
Aside: When I was "coming up", most of us couldn't afford a separate A clarinet when we needed the low Eb, so we transposed the A clarinet parts for Bb clarinet and borrowed instruments that had the low Eb key if we could. If no horn was available with the low Eb key and the music allowed it, we'd cut a piece of plastic or rubber pipe that, when stuffed into the bell, would give the low Eb when the low E was fingered. This only worked when we had the time to insert it and remove it, but it saved me several times playing the Sibelius "Valse Triste" and the Berlioz "Symphony Fantastique", third movement.
So let's say you'll only play band music or you don't have an A clarinet. why would you want the low Eb key? Well:
You can avoid the awful "throat Bb" fingering by playing the Bb with the low Eb key. Not only does it remove the problem of "going over the break" in fast passages, the timbre of the Bb now matches the timbre of the notes above it: lots of fingers down, improving the sound of the transition from Bb to B and above in the clarion register because all of the notes now are "long pipe" notes. No longer would you have to go from "short pipe" to long pipe over a break, with their stunning differences in timbre. (Tuning is better, too.)
Another aside: Believe it or not, my clarinet teacher, later principal of the New Zealand Symphony, played his entire clarinet career with a "full Boehm" instrument, which has the low Eb key. He never thought of using the key for the Bb until I suggested it to him! I contributed to my maestro's education, as lowly as I was!
Why don't we see these keys and mechanisms on most clarinets, or at least have them readily available as options?
Until a few years ago, no "major" clarinet maker offered them because they simply didn't want to offer options. And as players grew up or became used to not having them, demand went down, to the delight of the major makers.
As far as the articulated G# mechanism goes, the key work is more complex than for instruments without it, and your "non-specialist" tech either wouldn't or couldn't work on them mostly because the mechanism is a little tricky to deal with.
As time went by, all but a few players outside of Western Europe knew there was such as thing as the articulated G# mechanism.
People came to be able to afford A clarinets to hit the low Eb, but more significantly, they didn't have to learn to transpose A clarinet parts for the Bb instrument anymore, so the low Eb key was generally abandoned (much to the delight of makers with their eyes primarily on the bottom line).
Players, themselves didn't want to have to learn new fingerings, especially with the LH Eb/D# key, even though they'd be wildly helpful.
As far a rollers go, the only reason that I can think of why these aren't part of the standard clarinet keywork is to save money for the manufacturer.
There has always been a persistent myth that more keywork dulls the sound of the clarinet. This is another myth (never tested, only opinion). Yes, a fully keyed clarinet sounds differently than the ancient clarinet with only one or two keys, but adding one or two keys to a standard-keyed clarinet doesn't do much sound-wise. (There's a story here, which I'll relate at some point.)
Convinced you?
Several major makers now offer the auxiliary LH Eb/D# key on their top instruments, so they're out there.
I'm only aware of one non-custom maker that offers the articulated G# mechanism as standard on their models, Patricola.
If you've got the money, most custom makers such as Rossi, Wurlitzer, Schwenk & Segellke will add any kind of keywork that you ask for as options.
To my knowledge, key rollers can be installed by specialized clarinet techs, but no manufacturer outside of a couple high-end makers like Wurlitzer offer them as options.
Had enough? Me too.
Cheers!