First, the mantra in the Highway Code is actually Mirrors (plural), Signal, Manoeuvre. E.g. if turning left you check both the central and left mirrors.
Second, I'm not comfortable with the concept of a request, except in some circumstances. A manoeuvre which needs other drivers to change speed or direction should be the exception rather than the rule. For example pulling out into, or crossing, a seemingly never-ending stream of traffic.
I find I rarely make a turn in a built up area at 30 MPH, forcing following traffic to slow or, if there is sufficient width, to overtake.
The Highway Code suggest we should make an effort not to interfere with other road users.
Put these together, in real life, my manoeuvre is going to disrupt other road users, it is in my interest to be sure they have noticed my signal and are preparing to accommodate me, if they have not, there is going to be, at best a near miss at worst a crash.
Mirror/s, signal, manoeuvre, assumes other vehicles will have noted the signal and be taking action accordingly, yet we know the quickest way to a crash is to assume you know what others are doing.
Adding a mirror/s after the signal to confirm traffic around is adjusting to my signal removes the need to assume.
Without the cooperation of those behind and around I cannot safely manoeuvre, to me, this all part of creating that bubble of safety (as TC4714 aptly describes it).
The asking for permission, from other road users is, an expression I use to counter the selfish attitude that appears to go with driving, and fits the idea that we must cooperate if we are to drive safely together on the same road.
In practice, I cannot manoeuvre safely without knowing those around me have made the adjustments required or in other words, they have given me permission.
As I see it, to manoeuvre without permission means swapping the safety bubble for a bubble of chance, and as we know I can flip a coin and get heads several times but eventually it will land on tails.