Maximize DPS? PLD, hands down. 1-2-3 rotations + Spirits Within and Circle of Scorn whenever possible = max DPS. Oh, and use Fight or Flight after savage blade with SW and CoS on cooldown, and swap to Sword Oath when not tanking anything (but don't switch after a Savage Blade since switching interrupts your combo). A monkey could maximize DPS on a PLD. Doesn't mean the monkey would be a good tank, but that wasn't the question xD
SCH would be next easiest. Just dot everything with Cleric Stance up while healing, and drop Shadow Flare when you don't need Sacred Ground up (they're mutually exclusive). Oh, and run Selene instead of Eos for max raid DPS. This is easier than WHM because WHM have to switch stances much more often, and WHM can only either heal or DPS FFXIV gil at a given time. Due to SCH dots and pet, SCH is always healing (via the fairy) while actively DPSing and always DPSing (via DoTs) while actively healing.
Answering the actual question (which DPS is easiest to maximize DPS with), in a raid situation, BRD is easiest to max DPS. They do low DPS compared to other classes (if they're playing correctly and singing as needed), but maximizing their DPS is easy, and you can dodge raid mechanics while doing full DPS.
SMN is second easiest after BRD in raid situations. In a raid, there are usually few enemies, so DoTing them is easy. There's some complexity to MP management and pet management, but really, it's just DoT, contagion, fester, ruin, ruin, fester, ruin ruin, etc. In my (biased) opinion, SMN is complex when dealing with large crowds (like in dungeons), but easy when dealing with bosses (like in raids). And, since nearly all of the SMN damage is from DoTs, instant spells (like Fester and Ruin II), and the pet, they can do almost full DPS while moving. SMNs are terrible at dealing with weak adds though, unless they adds spawn close enough to the boss to Bane the boss's DoTs to them.
To maximize damage as a BLM, you have to know when move-requiring attacks are coming and time everything you do appropriately, which takes knowledge of the raid and practice. While BLM have the easiest rotation, they lose more DPS from moving at the wrong time than any other class.
MNK, NIN, and DRG all have complex rotations making them much harder to max DPS on than the ranged DPS. DRG have a complex rotation (tons of OGCD attacks to weave in and many short duration buffs/debuffs), but they have practically no positional requirements. MNK have a simpler rotation (some short duration buffs/debuffs and OGCD skills, but fewer), but nearly every attack of theirs has positional requirements. NIN has no positional requirements, but has to constantly use OGCD abilities (mudras, among others) to max DPS. NIN is probably the easiest out of those if you don't suffer from mudra lag, but with mudra lag, it can be hard to max DPS on a NIN.