P.G. Woodhouse famously transferred adverbs to be an adjective of the object - "he smoked an nonchalant cigarette", but I suspect that even he might struggle with the concept of a court hearing being harmed.
On conviction, the court are bound* by law to order your licence to be endorsed with either 3-6 points or to ban you from driving, The court also has sentencing guidelines which they are not strictly bound by, but would need to justify deviating from. Sentencing for speeding is largely paint by numbers, although mitigation can be considered.
Their guidelines for 41-50 are 4-6 points** and for 51+ are 6 points or a 7-56 day ban. Ordinarily, you would be almost certainly looking at 6 points. The courts have specific guidance not to issue a short ban to enable the accused to avoid a revocation under the Road Traffic (New Drivers) Act 1995.
The court could give you 5 points to enable you to avoid revocation if they considered it appropriate to do so. Whether or not they would be likely to is entirely down to them on the day.
Absent coming across as a "weapons grade Karen" and telling them that they *can't* give you 5 points as you are too important/entitled, it is difficult to see how the proposed letter would harm you case, other that it would almost certainly require an in person hearing to stand any chance of persuading the bench to step outside of the guidelines, as opposed to dealing with everything online/by post.
"I appreciate that your worships' guidance is to give me 6 points, which will result in my licence being revoked, but I would respectfully ask you to consider.."
* Absent special reasons not to endorse which concern the reason the offence was committed, not the effects of the punishment. And didn't see the sign (assuming that it was there to be seen) wouldn't cut it.
** The guidelines include the option of a 7-28 day ban for 41-50, but absent serious aggravating factors, very unlikely. Not applicable to your case anyway