We do practice that tai sabaki technique from the Enshin clips in our KK drills as well, but when it comes it to sparring and fighting it's a lot more head to head. Of course, those kinds of fights tend to look different because both fighters have had training and are less likely to lunge into a compromising position as would the angry brute on the street.
The best karate teachers will tell you that a real street fight won't look like anything you do in the dojo, should you ever be involved in one.
However the concepts you have ingrained will always follow the 'rule' of 'operant conditioning'…meaning you will subconsciously move and do in ways resembling your training, not exactly the same but in a similar 'ball park' of action. If you never trained those concepts you'd be a stick in the mud or the proverbial 'wall flower'_
This can be seen in trained athletes playing contact sports.
And here I speak of experience, both in sports and real life engagements.
I like your suggested drill of practicing defense with your back against the wall to develop lateral movement. Boxers practice circling around a ring all the time and they are very good at it. They love moving to the side and throwing a hook to the head or the body and they have a sense of timing for it that the average karateka lacks.
Many good teachers teach and practice the 'against the wall' drills.
The manner in which I teach them is to habituate a student to ingrain certain patterns of movement and tactics:
1. With your back to the wall and free space to your right and left sides we practice lateral take off against kicks, punches and grabs, flanking the opponent.
2. I then place objects directly to the sides of the student against the wall to prevent side to side movement but leaving the oblique clear, such as the diagonal angles to 10 an 2 o'clock.
This forces the defender to 'slide by' an attack in forward angles, using the protective moves of our wauke in ways to avoid while sticking to the attack, then turning to get behind the opponent and slam his head into the wall aided by his momentum.
Another inherent application in this angled take off is the trailing leg shin smashing into the opponent shins as you move diagonally.
3. I then block all possible angles of motion for the defender against the wall, who then must develop the concepts of pre-empting the attack upon sensing it coming, by attacking the attack, and or quickly blading the body as in the 'swinging door' aspects found in our kata.
4. But the most important 'technique' to develop, when up against a wall, is the one to sense 'something coming' and move to create distance before any attack has had a chance to materialize. The most difficult.
Again, the well practiced student, understands completely that none of what he does in the dojo will look or 'emerge' the same in a real encounter...
But he knows that the concepts will, another reason why the best teachers teach conceptually.