Looks like everyone is overlooking the value of splitting your damage across different attacks. Against low-hp enemies, this means potentially dropping an extra enemy each round.
No one is. Rather, everyone is looking at things like Frenzy, War Priest, Great Weapon Mastery (cleave works awesome against low hp enemies) and Polearm Mastery, where you can usually pull off a bonus action attack with your main hand weapon, so that you are getting the same number of attacks as fighting with two weapons, but superior damage on each hit. They're looking at Hex and Hunter Marks, which use up your bonus action to mark the enemy and are a main part of the playstyle of the appropriate classes. They are looking at class features like Cunning Action, Beastmaster, and Shield Mastery that also use up your bonus action to do non-attack things that are fairly cool.
One thing, when you're considering TWF is this - access to the Two Weapon Fighting Style means that its on par with a bonus action attack from Polearm or Great Weapon Mastery - the two feats auto add on your attribute for damage with bonus action attacks, while the default rules for using two shortswords don't. If you're not a class with that fighting style, and you have access to heavy weapons, then chances are that getting the feats are flat out outshine TWF so greatly. Very few people like being so clearly outshined - most want competitive choices, even if it does slightly less damage. Coupled with the need for two magic weapons and attunement rules, two weapon fighting has issues when faced with a heavy weapon feat's bonus action attack.
Two weapons works well with the fighter, given the limited number of bonus actions he has. Pretty easy to work with him. Plus, TW FS. I believe this is the only class where the style actually works well.
The Barbarian could theoretically pull it off, but the class requires you rely on Strength attacks, which negates the main advantage of TWF over two-handed weapons - the initiative bonus and potential stealth options. And I don't know anyone who'd go with a TWFing Berzerker with Frenzy right there; they wouldn't want to completely negate a class feature so thoroughly like that. So, that just leaves one subclass.
Skalds could do it - assuming you had breaks between giving out Inspirations, the occasional Healing Word, or you can fit it in with the spells you pick at level 10, should you get that far. A lot of competition for bonus actions makes it difficult to pull off.
Clerics depend on Domain, and if you're willing to juggle things instead of just putting a holy symbol on your shield. And you're not relying primarily on being a caster during most of your turns, which you should be doing. Kind of the point of being a full caster. War domain, the most weapon-dependent domain, as a feature for bonus action attacks. Attacking just isn't a major part of the class.
Druid doesn't TWF, moving on.
Monks use their own rule systems for multiple attacks, and not two weapon fighting. Thematically, you are fighting with two weapons, and likely the best class to pull off the style if you really want it.
Paladins. Designed for heavy weapons or sword/board. Zero incentive for going with two weapons.
Ranger - theoretically, it wants to allow TWF. It really does. But the weapon spells are a critical part of the class, and the vast majority of them use bonus actions. Beastmaster eats up either your full action (no attacks at all) or your bonus action (no off hand attack), so pointless there. So, unless you're using the spell-less ranger, the class doesn't really support the two weapon fighting style.
Rogue - as a backup if you miss with your main weapon and don't have something better in mind with Cunning Action, it works. Generally, I find that, should the first attack hit, most people ignore their off-hand weapon and Cunning Action something else. Technically, its wielding a second weapon, but it doesn't see much use. Its just... there. Over half the time, it doesn't feel like you're two weapon fighting.
Sorcerer - Going to have to look at Favored Soul closer, but I don't know how that class plays with buffs and quickened cantrips you'll likely be using, and how much you'll need an offhand arcane focus. That subclass is still being playtested.
Warlock - Even the bladelock has zero support for two weapon fighting, from the fact you can only pact-bond one weapon, to Hex being bonus action, to needing a free hand for spellcasting/rod/etc.
Wizard - nope.
There's a lot going on here beyond just "spreading out the damage."