The ordinary meaning of appreciate, as a transitive verb, is to form an estimate of the worth of anything, to set a value on it. It is therefore not surprising that it is useful to polite officials corresponding with members of the public who want more than they can get, as most of us do to-day. Refusals are softened by such phrases as "I appreciate how hard it is on you not to have it", and "you will appreciate the reasons why I cannot let you have it": Whatever the reason, there can be no doubt that appreciate is being used by the writers of official letters and circulars with a freedom that passes reason and needs to be curbed. An effective way of curbing it might be to resolve never to use it with a that clause ("I appreciate that there has been delay"), but always give it a noun or noun clause ("I appreciate your kindness").
Sometimes the word is used merely by way of polite padding as in:
You will appreciate therefore that the earliest date the department can release you is . . .
It will no doubt be appreciated that this cannot be reserved for an indefinite period.
The first might just as well have begun "The earliest date therefore" and the second "this cannot of course be reserved . . ." or, if that seems too abrupt, "You will no doubt understand that . . ."
Appreciate is often used where it would be more suitable to say understand, realise, recognise, be grateful, be obliged.
"It would be appreciated if" can usually be translated into "I shall be glad (or grateful, or obliged, or even pleased) if . . .". "You will appreciate" can often be better expressed by "you will realise ", or even "of course". Here are extracts from two letters that say the same thing, one with the help of appreciate and the other without. The one that does without is more natural and vigorous:
I fully appreciate that, in the circumstances you mention, a telephone would be a great convenience to you.
I realise just how useful a telephone would be to you.