Nice post. Love me some tactic debate
But first off, some semantics: A Libero is not a sweeper; well he is kind of but that only describes half of his role - namely the defensive one. Lacking a direct opponent on the pitch, the Libero is heavily embedded into the attacking game and covers vast amounts of space to serve as a deep lying playmaker, open man in midfield or even in the last third of the pitch.
Seeing his offensive role, it's clear that Barca already has such a player. It's Busquets.
Contrary to what someone stated, a Libero must have a wide array of skills; which means that one needs an elite player to play this position. Pace, endurance, vision, a deep understanding of the game and technique. Franz Beckenbauer, Horst Blankenburg, Ruud Krol, Gaetano Scirea and Matthias Sammer - all of which were known and famous for their classiness and technical skill.
Furthermore, the Libero of the past was the leader on the pitch, both offensively and defensively. He was a 'free' player for all intents and purposes; which also meant that other players weren't
as 'free'. With the Libero moving up the pitch, either a holding player or a midfielder had to be sacrificed to cover the Liberos' position in defense. In modern football, especially Barca takes a leading role here, each player has both offensive and defensive tasks and duties. The game is 'democratized', if you will. Fielding a Libero means altering the entire style of play.
Now that we've established what a Libero is and that Libero =/= Sweeper; let's assume that Barca would field a sweeper staggered behind a 3-man defense: For multiple reasons, this can't work.
1. The offside trap: Barcas' high line of defense requires the efficient use of the offside trap as one of many means to suffocate counter-attacks. The Sweeper behind the defense was (arguably) established by Herbert Chapmans' Arsenal in 1925 as an answer to the modified offside rule and became quite popular later in the italian catenaccio. Yet naerly none of the teams at the time, or in later years for that matter, fielded such a high line of defense as Barca does. Doing so requires the defense to be on an almost straight horizontal line, which can't work with a sweeper. That's why high intensity teams like Sacchi's Milan abstained from fielding one and instead chose a back-4.
2. High pressure: Fielding an
additional sweeper means sacrificing a player. In order for efficient counter-pressing to work local majorities have to be created with an efficient use of 'covering-shadows'. One less player up the pitch means one less player to press, which results in less efficient use of coverering space.
Using a sweeper as you described, someone who basically covers the FBs' position when he (the FB) is moving up the pitch, there would be no notable difference at all to what the team played under Guardiola. Because again, that is/was Busquests' part. Nevertheless, it means sacrificing a player which is arguably (!) more efficient higher up the pitch in a counter-pressing effort.
3. Attacking: The flipside of the defense coin. One FB going forward at a time means an asymmetric and therefore predictable approach to the attacking game. Don't get me wrong, both FBs' bombing forward all the time isn't the solution and symmetric play isn't by nature preferable. It's just that a different form of asymmetry should be aspired. One FB working the vertical, while the other FB is moving forward diagonally, as seen vs Milan and many times before when Abidal played LB, provides enough width and also a distraction.
4. Busquets: I mentioned him before and here's why: He
is a modern-day libero. Not in the sense of being staggered behind the backline in the formation, but because of what he does. As long as his role is clearly defined and he finds a balance between his offensive and defensive duties, which wasn't always the case, there's simply no need to field a sweeper.