What makes side quests interesting? If you're making a fantasy RPG but you want to keep things "serious" you're obviously limiting yourself in what you can do. Defiance Bay suffers a lot from this, you just have to compare it to Athkatla to see that. An undead making machine is nothing compared to having a gang war with vampires, though that is also a problem of scope. But things like Pernisc's or the Salty Mast's quest are as banal and predictable as they come.
BG's world seemed well-realised because it integrated the fantasy elements well. In PoE they stand out like a sore thumb.
Humour and silliness aren't synonymous with wacky in this case. I take wacky here to mean anything requiring suspension of disbelief. However, seriousness stumps suspension of disbelief, so silliness can enhance the fantasy aspects (within limits).
The points you mention would make for a more cohesive/ convincing gaming experience, but I don't see anything there that would require throwing the term soul around. Games can be a polished experience without anyone talking about soul.
For me "interesting" is a presentation of personal or relatable problems or situations, that is at one with and hopefully enhances the gameplay of a quest. It can be as deadly serious as say Vault 11 in New Vegas or the backstory of Durlag's Tower, or as lighthearted as much of Torment was, so long as it is implemented well. Defiance Bay I agree was not as well realised a setting as Athkatla, and nowhere near Vizima, Britain, Tarant or Sigil, however wackiness had nothing to do with that, it was more a case of a lack of focus on the little touches that aid verisimilitude, and the lack of thematic reinforcement.
BG was alright, however as a setting the Realms are hardly attractive and as vanilla as they come, and I would not say any element was presented well, it is a renaissance fayre setting with a thin veneer of out of place cultures. The setting of Poe definitely needed exploring and expanding upon more, I would have cut almost half the games locations that are nothing but backdrops for grinding and detailed the remainder with far more depth and reactivity. There is interesting worldbuilding in Poe, it needed to be brought to the fore and examined.
Seriousness does not stymie suspension of belief, quite the opposite, it enhances a gameworld if it has verisimilitude, if the inhabitants show realistic behaviour and the issues of the world are well presented. Silliness is alright for silly situations or for breaking tension, if always used in a serious situation however it is likely to become vapid squeeing, out of place, childish and unrealistic. Morte serves as a counterpoint to the grim, driven and serious tone of much of Torment, the lighthearted and serious being well used, but even Morte's quips fade when the issue of his lying is brought up and the past is remembered. Seriousness has a place just as much as any other element, and many fantastic elements are not just serious but horrifying or outlandish in the extreme.
I used "soul" because it was used in your opening argument, I find it too nebulous a term personally, but I would argue that a cohesive and convincing experience goes a long way towards making the player feel the gameworld has "soul." I would use Arcanum, Betrayal at Krondor, Fallout, Torment, the mid Ultimas and the first Witcher as games that were cohesive, presented fantastic elements well and reinforced their thematic messages through gameplay and features. I think you are focusing upon the wrong problems in Poe, I do not think it lacked fantastical elements, or what you term "wacky" ones, I think it did not present them well enough, did not explore them, and did not plant the priotagonist firmly enough in the midst of them.