We must always remember that the 'sound in mind' is in the mind. Often by necessity. Beethoven? A composer writing a symphony or opera score at his piano has little to do with the orchestra, at the time of his writing down the notes.
I like the idea that music is made by sounds and not notes. An 'objective measure' of a composition would be to count the notes, stopwatch the timing between the bars, possibly count the repetitions and frequency of the various notes, and count which were used more often. But that would have nothing to do with music.
Some listeners go this approach. I remember reading an analysis of some opera recordings by Dave Ranada. He made a spreadsheet of a half a dozen recordings, listing timings, etc. I was scratching my head. I was asking, "What is all that telling him? Why is he doing that?" Really, anyone can, within a few short bars, compare Toscanini to Furtwangler, and immediately (intuitively) discover who is conducting at what tempo, and (depending upon one's mood) determine which conductor has a better grasp of the 'notes on paper'.
Oh, yes, Toscanini vs. Furwangler--Opus Magazine (RIP) had a long series of articles and letters to the editor on the whole Beethoven Tempo Debate back in the late 80's or thereabouts. I do like Beethoven at the tempo Beethoven marked, and I do like the music punctuated by the sforzandos that Beethoven used, rather than the extended smooshiness (technical term) that Beethoven had become as interpreted by post-Wagnerian conductors (like Furtwangler). It just makes the music more lively and less heavy. I think it was in that debate that Norrington made his observation that we play stuff the way the composer marked it so that it would sound new again.
But some of those post-Wagnerian conductors could produce real magic, too. Cellibidache (rarely recorded), Fricsay--some real magic came from those batons from a range of composers.
A more interesting comparison to me is the way in which Adrian Boult and John Barbirolli conducted Vaughan Williams. Boult is careful and disciplined, and Boult is all over the map. (I have a 1958 recording of Barbirolli conducting the second symphony, compared to a 60's recording by Boult). Vaughan Williams thought of Boult as a good friend, but his term for the other was "Glorious John!" That tells me that composers are not necessarily that picky about the details. Vaughan Williams himself conducted (or directed the conductor to--I don't recall) his third symphony (Pastoral) a bit more quickly than he really wanted to at the premiere, because he though the audience would not tolerate three slow movements that were that slow. He became more committed to the slow tempi when others conducted it effectively as marked, as I recall the story.
But on the topic of Ralph Vaughan Williams, I do not need to again hear his Tuba Concerto on the ancient-design tiny Barlow F tuba that was used at the premiere. When John Fletcher, Roger Bobo, and other greats of the 60's and 70's recorded it, the music blossomed with lovely tone and musicality. The great Arnold Jacobs recorded it with Chicago in the late 60's, and purposely used a British orchestral F of the type used at the premiere, I think he did not get the effect he was certainly capable of.
Rick "the answer to the OP's question: it depends on what serves the music" Denney