Having good FBs is a major boon...but they're less important than CBs, they are less important than midfielders, & they are less important than attackers
There's a reason most high-end FBs played more important positions at youth levels before moving to FB as pros.
You take out Marcelo and Carvajal out of Real, replace them with Theo Hernandez and Achraf (as was the case this season) and its no longer the same team. I mean, even a struggling Marcelo or Carvajal made that Real squad look so pedestrian in the first half of the season.
They're THAT important for them.
The modern fullback is force on both ends of the pitch, and absolutely vital in transition. They need to be defensively adequate to basically play CB when the ball is on the off-wing, they need to have the stamina and speed to make the most sprints in the match, and their average KM run has climbed up so much that they're almost up there with midfielders right.
The modern fullback is no longer a Gary Neville, a very limited offensive player, but a fixture in any Man Utd or England side in his playing days and a great player in his own right. Not even a Maldini, probably my favorite player of all time (even though I grew up a Juve fan).
Its a Marcelo, Carvajal, Lahm, even Ashley Cole, etc.
It is true, and you're right, that they were very dull 20 years ago, at least those fullbacks in a 4-at-the-back.
A lot of continental teams used wing-backs with 3-5-2 that was so popular across Germany, Italy, Croatia, etc.
In a 4-4-2 teams used a Tassoti, Maldini,Thuram or Neville, in a 3-5-2 teams used a Robert Jarni, for example.
God I miss Jarni, we've seen nothing like him in 15 years here (speaking of Croatia).
Very few fullbacks were bombing forward in a 4-at-the-back, or had the capacity for it (Cafu and Roberto Carlos, for example).
Here's a decent, though very superficial article on fullbacks and their growing role in the game, including some data - though sadly only about the Premier League:
How full-backs became football's most important players
And again, if your fullback is not up to par, defensively or offensively, your midfielder and winger have to cheat to that side, creating a "bleed" on the pitch.
Last season's Barca was a perfect example.
FWIW, I played CB, and when my starting LB was injured or something, and replaced by an inferior player, it's a different game.
You start cheating to his side, trying to protect his back more than usual, etc etc. - and that's just defensively.
Anyway... TLDR; IMO fullbacks have become absolutely vital in modern football, yes. Partly because they're "more than fullbacks" today.