How scarce are souls?
Yes and no.
Basically, after a while (as you mentioned), enemies stop spawning. So the souls stop flowing. However, there are ways around this.
- Infinitely Spawning Enemies. Yup, you heard right. There are enemies that infinitely respawn; primarily the Stone Soldiers in Drangleic Castle.
- Bonfire Ascetics. Using bonfire Ascetics is a great way to farm souls, as once enemies stop spawning, this resets their cycle. The catch is: increased souls, and increased difficulty.
With the latest patch, Dark Souls 2 gives you unlimited souls, available near the start of the game.
This is due to a change with the covenant Company of Champions, accessible when you reach Majula (within 5 minutes in a new game).
In particular, one of the effect of this Covenant is as follows:
Joining this covenant will give all non-special enemies unlimited spawns for the duration you're in the covenant (special enemies such as the Aldia Warlock in Shrine of Amana or the necromancers in Huntsman's Copse will not respawn).
Once you leave, all enemies will return to the spawning condition they had before you joined.
This change was relatively recent. It was updated after I have beaten it, but I noticed it during one of my more recent re-plays.
Note: Joining the Company of Champions is effective doing the same thing as burning a bonfire ascetic, except you can leave the covenant and reverse the upgraded enemies. If you want to know how tough an area is after burning an ascetic, try out the covenant and test it out.
Just to make the topic complete. Another infinite source of souls is White Soap Stones. By helping others to kill bosses and other enemies you get your part (up to 50%) of the souls and it has no influence on enemies in your world.