So I’ll explain more:
As for dagesh — a strong dagesh requires the sheva to be mobile and not silent, because a strong dagesh is really a doubling of the letter. And when there are two identical letters, the second cannot have a silent sheva.
As for long and short vowels — basically, the vowels are arranged so that their length will be equal. Therefore, when there is a short vowel, it ends with a silent sheva that closes it (and actually also lengthens it). When there is a long vowel, it does not end with a silent sheva (because that would lengthen it too much), and therefore if there is a sheva after it, it will be a mobile sheva, which already connects to the following vowel. So in principle the rule is that an unaccented closed syllable (with a silent sheva) should have a short vowel (abbreviated: SALAK — closed, unaccented, short).
Since that is so — meaning, the definition of the sheva stems from the strong dagesh or from the length of the preceding vowel — my question returns: if in any case we are not careful about a strong dagesh and about vowel length, what is the point of being careful about a mobile sheva?

Hope I’m clearer now

So be careful about it. I myself started being careful once I understood how to pronounce a strong dagesh.

And assuming a person isn’t careful, or that if he starts distinguishing between a long and a short vowel he’ll never finish the prayer (that’s probably the reality at least for some of us), is there any point in being careful about mobile versus silent sheva (which is easier), when the distinction between them is based on the distinction between a long and a short vowel?

For me it was pretty intuitive once I understood how a strong dagesh is pronounced.

And what about a long and a short vowel?

And you can extend the question to the meteg as well (in the cantillation marks). One of the reasons a meteg appears is before a hataf. Since the vowel of a hataf is very short (even shorter than a regular short vowel), in order that it not get swallowed up, they added a meteg before it (the meteg is a half-stress).
But today there is almost no one who distinguishes between patah and hataf-patah, between segol and hataf-segol, and between kamatz katan and hataf-kamatz-katan.
So is there no value in being careful about pronouncing the meteg (in these cases)?

I’m not careful about those things either. Among Sephardim, some are careful about them. It seems to me that at the end of the day, if you have the distinction, then you’re obligated to keep it, and if not, then not.

To Y.D.,
I’m not sure you understood the root of the question. I’d appreciate it if you read it again. It concerns the fact that grammatical rule A derives from grammatical rule B, and then the question is whether there is any meaning to being careful about A when one is not careful about B.

It seems to me that in any case it’s better for the word to be as close as possible to the original.