It's not that unthinkable that Kojima's grand ambitions ran into budget constraints and they had to cut down the story content. I can easily imagine dozens of more hours of voiced and animated cutscenes polishing out the content that's already in there, but voicing and animation are expensive.
What remains is imho still quite good and entertaining, I really enjoyed the open world parts, the base management, hunting for new soldiers or grooming favorites.
The multiplayer part made it all a bit grindy, without some story fluff in-between, but I think it was a smart game mechanic to add to a sneaking game where you have the option for non-lethal take-downs/straight up bypassing of enemies, especially in the context of the "lore".
But having at least some of these tapes as actual cutscenes would probably have changed a lot about the game feeling "unfinished".
A lot of important main story beats are revealed through those tapes, of which there are so many that going through them feels like a chore at times.
That's probably why so many people consider the game so light on story: Those tapes are easily skipped by players so they can progress further through the game, but barely anybody would skip a full blown cutscene with said tapes content.
But on the other hand I got the impression that the game was definitely not finished plot wise and even stylistically, at least not to the point that Kojima and his core team had originally envisioned. It felt like we got 90%, but that last 10% was the bit that was supposed to fill in the gaps in the plot and leave the player feeling satisfied. Compared to e.g. the ending of MGS4 (which is my favorite in the series), the latter third of MGSV was just so... unfulfilling.
I suspect friction over Kojima's vision versus Konami wanting to get the game to market was why they parted ways, even though Konami was very clearly killing the golden goose.