Generally, when "stand" is used to mean "is in a standing position", it is accompanied by a location:
He stood in the corner, sipping a whiskey.
They stood around the table, arguing.
She stood by the window, looking forlornly down the empty driveway.
Often this meaning will be expressed in the past continuous, using "was standing" instead of "stood" to unambiguously refer to the condition of standing, as opposed to the act of standing:
He was standing in the corner, sipping a whiskey.
When "stand" is used to mean "get to one's feet", it is either unaccompanied, or accompanied by an event:
He stood when she entered the room.
They stood as the speaker finished his speech.
"Now that you're here, I can finally leave," she said as she stood.
In my experience, stand up is rarely used for "be in a standing position" when it refers to a person; you are much more likely to hear it used for an inanimate object (especially one which is normally horizontal), and again it will most likely be accompanied by a location:
The bedframe stood up against the wall.
Most often, stand up is used for the action of getting to one's feet:
He stood up and stretched
As I approached, he stood up and reached to shake my hand.
Everyone stood up when the orchestra finished its song.
In your first two examples, people changed from sitting to standing when the president came in, and people changed from sitting to standing for the opening of the speech (they did not remain standing for the entire speech, but sat down again after only a moment or two).
Your given alternatives, "get to one's feet" and "rise", both unambiguously refer to the action of changing from a non-standing position into a standing position.
- I can't make it home CORRECT
This means you are unable to reach this destination. Home could refer to the building, or the area where you live; e.g., village, city, country. When used as an adverb of place, home requires no preposition
An Australian holidaymaker: I can't wait to get back home (home = Melbourne, Australia)
- I can't make it to home UNLIKELY but not impossible
In this sentence we have to identify what home might be referring to. It could be short for home base (think of a baseball player running to home base) or the home plate
With the Yankees prepared for the long play, Taylor instead bunts, allowing Hayes to make it to home safely and win the game.
- There was heavy traffic but I finally made it to work CORRECT
This means the speaker managed to arrive at his or her workplace despite the traffic. Work and workplace are nouns, and the preposition to is used to express motion or a direction toward a point or thing.
- There was heavy traffic but I finally made it work INCORRECT
This sentence is grammatical but it has a completely different meaning. It means that the speaker managed to make something work i.e function despite the heavy traffic. In other words, the speaker repaired something that was broken or not functioning properly. And in the sentence, work is used a verb
My watch is broken, can you make it work again?
His phone doesn't work unless he goes to a high point
Best Answer
In your first pair of examples, for and because of are equivalent semantically, unambivalent, and correct grammatically.
However, in your second pair, the second option is preferable
This is because in the first option
there is a subtle ambiguity in the meaning of "for": We resolve it because we understand "heavy traffic" as something that can cause someone to be late. So we assume this is the "because of" sense of for, as in "You can't see the forest for the trees".
But if you didn't know that "heavy traffic" is undesirable, you might parse it as:
To better see how much this depends on the meaning of the NP that follows "for" (i.e., "heavy traffic"), we need only replace "heavy traffic" (a known hindrance) with a desirable event:
We have no problem understanding that either. It means they were going to the party, and did not arrive on time. Of course, this is a different sense of "for". But it's the same syntax!
Now if we try to replace for with because of, look what happens:
Now we are not saying that they arrived late at the party; we are saying that they arrived late at some later, unnamed event, because they had been at the party.
So yes, there are cases where you cannot replace "for" with "because of".
(And there are cases where you not only could, but ought to)
Your second pair of examples are actually that type of case, syntactically—it is only semantics that allows a native speaker to discern the intended sense of "for".
Suppose we phrase it this way:
This is unambiguous, though it would be considered quaint or overly formal (in AmE).
But if we rephrase this same idea, in the simpler and more idiomatic style below,
we see a clear distinction between the usage of "for" and "because of". You could NOT replace for with because of; nor could you replace because of with for.