Yeah but why should I? A tighter chamber is more time consuming and telegraphed, and it doesn't make my form any worse or better, just more or less pronounced.
It does so at the expense of power and often height. Those may not be important for what you're using for (maybe sparring), but they are normally how they're used in Kukkiwon Taekwondo.
Not so... Grandmaster Woo teacher front chamber
OK, so there are two things I'd like to discuss here.
When I said "Kukkiwon instructor" I didn't just mean "Instructors of Kukkiwon-style Taekwondo", but I meant official Kukkiwon Instructors - those that teach on the master instructor and poom/dan examiner courses. Considered by the Kukkiwon to be the best of the best.
Secondly, most instructors advocate when demonstrating/learning step-by-step putting the knee forward first. However, when doing it fast/full speed, they don't actually do that. For very good reason, you throw momentum forward to bring it back (when rotating to chamber) only to then try to throw it forward again. So conservation of momentum gives a good reason for not going forward-side-kick, only going side-kick. We've stopped teaching this way in our club because it is actually needless.
If you watch Grandmaster Woo's video, go to any of the full speed kicks (about 2:55 onwards) and pause the video. Then use the comma and full-stop/period buttons (same keys as < and >) to go frame-by-frame, you'll see it's performed differently to how it's done when performed step-by-step.
Almost all Taekwondo side kick videos are the same - when done step by step it's knee to the front, then rotate to the side and then kick. Then you watch the fast ones, go frame-by-frame and notice they don't actually go to the front, but rather rotate quickly and take their knee through and straight to the chamber position.
However, if you then watch Grandmaster Kang, Ik-Pil's video, you'll see that he actually does it the same way as he teaches - forward first. However, he doesn't advocate getting as tight a chamber as most other Kukkiwon instructors (and international masters). He prefers to go for pure linear momentum than the rotation to chamber and extension.
I've discussed this with many grandmasters and masters, and they 99% (GM Kang aside) say the same thing - forward, rotate, kick. Then I show them a video in slow motion of them doing it and get a "oh yeah, it doesn't actually go forward". I've had this conversation in English and Korean (I'm a lower-advanced in Korean), the same every time.
Here's another video that shows it step by step (going forward) then in slow motion during an actual kick and the knee never goes forward:
Hope this helps explain.