I mentioned this in another question, but just because the morphological inflection is disappearing, that doesn't mean the subjunctive mood is actually disappearing from the language. Just like when most of our verbal inflection disappeared (now it's "I go", "you go", "we go", "they go"), that doesn't mean we lost verbs for first person singular and plural, 2nd person, and so on.
Nohat's short answer gives the main point — if 9 out of 10 times the form looks identical to a MUCH more common form, then over time things might converge and regularize. A linguist would call this "paradigm leveling". Less common words and structures tend to regularize faster than more common ones (which is why words like "to be" and "to have" are irregular in so many different languages). The subjunctive is rare and not that distinct in English, so it is in trouble.
We see the past subjunctive form only in "to be", but we see the present subjunctive in the third person singular form of any verb — it has no "s" at the end like the indicative form.
So, this is of course subjunctive:
If I were ten years younger... (often said "If I was...")
But this is subjunctive too:
So be it.
It's important that he arrive on time tomorrow.
There are a bunch of examples here that include this other kind of subjunctive. This is just anecdotal but I haven't noticed this one disappearing as much.
Is this a general trend in related languages? Well, in Swedish this seems to be happening. In German one subjunctive form is used all over the place, and the other is used pretty much just in newspapers and journalism in general, but it is at no risk of dying out (it has legal implications akin to those that make the word "allegedly" so important in English journalism).
Short answer:
- It switches to were for "wish" statements because were is acting as a marker for such statements, rather than an actual past tense verb.
- Comparisons between middle/early modern English and today's English are tough to make, as no language is static. We've consistently been losing the case and inflection system from English for centuries (When was the last time you saw "Olde Shoppe" when it wasn't an obvious throwback?). As a result, what is proper during Shakespeare's time, and proper now, are two very different grammar codes for writing.
Long answer:
Most languages, especially older languages have a number of cases (nouns) and inflections (verbs) that English syntax has subsumed. For instance, in biblical Hebrew, A number of Greek variations, Latin, etc, the difference between the subject and predicate noun is clearly marked (not always so in biblical Hebrew, but still pretty common). Specifically to this question inflections changed in verbs creating the Subjunctive (possibility) and the Optative (slight possibility) tenses, in Greek; the Jussive (expression of command) and the Cohortative (exhorting a person to do something) in Hebrew; etc. In English, these have mainly fallen away, replaced with sentence placement and modals, though some are still dependent upon case-forms.
So, a sentence based on a modal and syntax might be, "We could go to the store today." It is based on syntax/position because this (admittedly stilted sentence) "Go to the store today, could we?" is now asking for permission, even though the same words are used without changes tenses.
For nouns, we can see it in: "Who is going to the store," and "You are going to the store with whom?" is an example of "who" changing case form—from subject to object.
For verbs dealing with subjunctives, were has become a condition marker for what is essentially the Optative case—remote possibility: "if he were to win the lottery, I still wouldn't go out with him." Don't think of it as past tense anymore. While it uses the past tense of to be in the plural, it's now a marker for a different function of language.
Why then, do we continue to use the present tense in some subjunctive sentences? That is dependent upon the action within the apodosis (second part of the conditional sentence). To use your sentences:
"It is essential that she be present."
"It was essential that she be present."
The past tense is expressed in the protasis. But the action itself was stative. You're stating a fact that has no ending. A past tense means that the action has been completed. Thus, "she was present" could be used if she walked into the room, thus completing the stative verb. However, it would no longer be a subjunctive, because a subjunctive is not completed action. The present tense must therefore be used to keep the action open.
At least, that's how I see it.
Best Answer
Your last example - an indirect command or request - is quite common in formal contexts, such as minutes of meetings, and even in speech for some speakers, though many would say "that he files".
The other examples are much rarer: they are archaic, and few people would use them except in special registers. But anywhere you could use "If I be", you could equally use "If he jump".