Erikur is also noted to be indifferent to loyalties, as uesp mentions he is willing to sell to Stormcloaks also. Nobles in Skyrim aren't perfect, on both sides of the civil war. Skald isn't a great noble, Laila is politically weak. The Elder Council aren't mentioned much, so I hold off doubts since Erikur is merely a self interested Skyrim noble. Tullius' comment is powerful to be sure.
The Carvains seem to be lowly nobles, they're trying to secure an import deal and try gain an audience with the Emperor. Two people don't paint a province, same could be said for nobles like Silver-Bloods etc. Nobles are nobles, you rarely get good ones.
On the subject of the Carvains, they're harmless. Have come across them after you kill Vici? I nearly pissed myself laughing.
Salonia: "I hate it here. Those were my favorite shoes, ruined and for what? We never even made it to the wedding."
Plautis: "Wha... Your shoes? We get robbed by bandits, my clothes torn to shreds by some giant cat, our bodyguard eaten by a dragon... And you're worried about your shoes?"
Salonia: "When we get back to Cyrodiil, I swear I will hire an army of battlemages to come up here and set fire to the whole damned province."
Ulfric and Tullius are focused on their war. The Dragons are becoming a problem, as Tullius admits when you ask him so it means. They're becoming a problem. Tullius and Ulfric are stubborn.
The Forsworn are dangerous, even if they use sticks and bones. They attack settlements, trade shipments, travelers. Supplies are managing to go through, on roads the Forsworn don't attack. So if you don't control certain roads, that is an issue.
Some loose stones here and there? The homes are falling apart, walls are crumbling. It may be the oldest city in Skyrim, but unless you want it to be the oldest ruin it needs constant maintenance.
As for Balgruuf and his steward, the full quote for that is.
Proventus: "My lord, our provisions are running dangerously low. Our stores of meat, wine and grain are all but depleted."
Balgruuf: "Purchase more supplies, then. That's your job as Steward, isn't it? Why do you trouble me with these details?"
Proventus: "My lord, since Ulfric Stormcloak's uprising, the cost of goods has doubled. I'll need more coin if I'm to provision us properly."
Balgruuf: "Our coffers are nearly empty. I can scarcely afford to pay the guards, and we need every one of them in these troubled times. You'll have to make do with what we have, Proventus."
Proventus: "Yes, my lord."
Belethor mentions it. "Interesting, to say the least. What with all that's been going on. On the one hand, supplies are harder to come by, since fewer traders are traveling the roads these days. But on the other, the scarcity of supplies has led to some, well, 'elevated' prices. All that matters is that I have what you need. And it's worth every septim."
The Khajiit traders also mention it.
"The dragons and the war have scared many other traders away, but for those with courage, there is much profit to be made."
So the Priestess is lying? Should of known that when she said Talos be with you when Rogvir died. Stormcloak propaganda...
Need to obtain those supplies, need to restore the resources the war took tolls on. They can do it, but it'll be sometime and it won't be simple. It'll take a lot of resources to simply be able to keep the resources and keep Forsworn and Bandits from raiding supplies. Also with the lack of traders in Skyrim, be sometime before they all return.