The new jobs aren't really any more soloable than the others, but they've added a lot of things that make it easier to solo overall. A recent update adds an effect to Signet (and Sanction, the Aht Urghan equivalent) that makes it so you don't lose TP while resting as long as it's active. Red Mage is VERY soloable, especially with the right subjob, Ninja is relatively soloable if you know what you're doing, Dragoon is fairly soloable, with a few drawbacks, Beastmaster was practically MADE to solo with, Puppetmaster is indeed very easy to solo, but can and will become very expensive, and Blue Mage is very soloable early on, but gets very difficult to solo mid-levels (around 25-40ish) until you get the ability to self-skillchain/magic burst.