Cesc Fabregas seems to be a pretty divisive transfer target as his signing seemingly becomes more and more inevitable, because even leaving the whole Arsenal/Barcelona/him being bit of a dick thing aside, there's the debate about whether he actually fits into the Chelsea side.
First, though, there's the need to clarify something about the player some people believe Fabregas would be replacing, Oscar. Even though the Brazilian's played almost exclusively in the attacking band of a 4-2-3-1 since joining the club, we still have widespread calls for Jose Mourinho to switch things up to a 4-3-3, thus moving Oscar back into a deeper position and 'solving' the lack of creativity we have in deep positions.
The thing about this analysis, however, is that it neglects the fact Oscar is hardly shackled by playing number 10 in a 4-2-3-1. Rather, he's always on the move. There's actually little to distinguish between Chelsea's 4-2-3-1 and a '4-3-3-', because Oscar often drops into deep, right-sided positions near the centre circle to collect passes. Shifting Oscar deeper positionally wouldn't actually change much from an attacking perspective, because he would still receive possession in largely the same zones.
Secondly, and more pertinently, Oscar's a better fit for the central attacking role because of his defensive ability. Yes, he's excellent in that regard, especially when compared to other no.10s (like Mata), but there's a difference between his defensive attributes and, say, someone like Matic. Where the latter is stronger in terms of holding his position, occupying space and dispossessing attackers coming towards him, Oscar's more of a 'pack-dog': chasing, hounding opponents, pressing them into difficult positions and forcing awkward passes - thus making him an excellent fit in an advanced role, where he's close to the ball when it's turned over and allowing him to immediately set the tone of the press, working hard to win the ball back high up the pitch. Even when used out wide, Oscar is always weaker when tracking back and protecting his zone - instead, he's more comfortable moving towards the attacker, defending proactively.
Permanently positioning him deeper, as is often proposed, would expose the weaker side of his defensive game, without actually maximising his attacking attributes.
This, combined with the workhorse ability of Willian and Eden Hazard, and now, presumably, Diego Costa, Chelsea have the tools to deploy an effective high-pressure game, as they did to some extent in the first half of last season. That's the first consideration of any mooted Fabregas deal - while, yes, he may be defensively weak for a pivot role, he would be protected by the work-rate of the players ahead of him.
Secondly, in relation to the role of Oscar as mentioned above, Fabregas wouldn't be a 'pivot' player per se, because of the flexibility Mourinho implemented in his midfield triangle, made possible by the roaming movement of Oscar when Chelsea have possession. When Oscar vacates the number ten position to come searching for the ball in a deep position, it opens up space for one of the deeper midfield players to move forward - just as Ramires sometimes did, interchanging nicely with his compatriot so that even when Oscar dropped deep, Chelsea didn't lose numbers in advanced positions.
Furthermore, Chelsea's biggest issue last season was widely accepted to be their inability to break down deep defences. While Fabregas's defensive ability may divide, his technical ability remains excellent: he's very direct and purposeful with his passing, and is superb at linking with attackers with quick, incisive, forward balls. That's what made him so effective at Arsenal. He combines creativity with the urgency required in the Premier League.
That, though, caused problems when he returned to Barcelona. As Fabregas himself suggested, "I always want to get forward, as I was used to at Arsenal, where the football is more nervous. Now, my position is higher up on the pitch, sometimes I don’t touch the ball as often as I used to, so I have to be patient."
That would explain why Fabregas has never quite fitted back in at his boyhood club. There's no real position for him at Barca: he's not calm enough to play as part of their midfield trio, because his movement high up the pitch leaves the side undermanned in deeper zones, and thus unable to retain possession, as is their wont. He's also not suited to being higher up on the flank, although has had fleeting success as a false nine - generally, though, Barcelona have had to deviate from their beloved philosophy to fit Fabregas in, rather than the other way round.
That leads to a broader, more ambitious theory, wherein it's possible that playing for Barcelona can skew a player's ability. It's simply incredibly difficult to fit into their style as an outsider. Their system has such restricted, demanding roles - new signings have to fit in, or get sold. Their style of play is so radically different to other systems, it creates a warped view of the players abilities.
For example, Dani Alves's advanced positioning at right-back (ractically as a right-winger) would be an enormous problem (in terms of the space in behind) for any other side that didn't dominate possession as much as Barca - but because they give the ball away so infrequently, Alves has the freedom to push forward without fear of being caught on the counter. That, in part, explains the trouble with Fabregas at Barca - because he's more ambitious with his passing, the side has to transition into defence more often, thus exposing certain elements of their game. The Barcelona system requires very specific, exacting attributes, and not possessing those qualities doesn't make you a poor player.
In most cases it would be ridiculous to suggest a player's form four years ago is a more accurate depiction of their abilities, but in the case of Fabregas and Barcelona, it's a fair argument to make.
Beyond this point, however, there also seems to be the odd misconception that if we signed Fabregas, Mourinho would be unable to rotate the squad. If Mourinho agrees with the idea that Fabregas isn't defensively strong enough for Chelsea's midfield, then he can rotate for the big games where he feels like this would be a problem - just like he did last season by adjusting and putting David Luiz alongside Matic. It'd be very odd if Mourinho didn't accept something had to change regarding his approach to games against weaker sides, and Fabregas would be a good way of increasing the tempo and incisiveness of Chelsea's passing in deeper positions against parked buses.
There's no such thing as a 'starting line-up': you rotate and adapt to a multitude of factors in every game. In that sense, Fabregas adds a new, otherwise missing, option to Mourinho's squad, 'defensively strong for the pivot' or not.