The notion of a coherent topos is a somewhat "refined" finiteness condition to put on a topos. One reason it is considered a "fruitful" notion is the Deligne completeness theorem, which tells us that every coherent topos has enough points.
A much "cruder" finiteness condition on a topos is to ask that it be locally finitely-presentable. I say that this is less "refined" because the notion of local finite presentability is not specifically adapted to topos theory -- it is a widely used notion in category theory more generally, whereas coherence is a notion which is not well-adapted to the study of categories like $Ab$ or $Grp$ which are very far from being toposes.
Despite the "crude" nature of this finiteness condition, it turns out to be specifically relevant to topos theory, due to the theorem that a topos is exponentiable if and only if it is a retract [EDIT: in a sense! see Marc Hoyois' comment below!] of a locally finitely presentable topos. This continues to be true $\infty$-categorically.
Moreover, every coherent topos is locally finitely presentable, motivating the following questions:
Question 1: Does every locally finitely presentable topos have enough points?
Equivalently More strongly, does every exponentiable topos have enough points?
Question 2: Does every compactly-generated $\infty$-topos have enough points? (Answer: no, as pointed out by Simon Henry below -- parameterized spectra are a counterexample)
Equivalently More strongly, does every exponentiable $\infty$-topos have enough points? (Answer: no, a fortiori)
Remarks:
There is reason to think that the answer should be affirmative. For instance, the answer is yes if we restrict attention to localic toposes. That is, every exponentiable locale is spatial.
If the answer is "yes", then we have a great strengthening of the Deligne completeness theorem. In fact, if the answer is "yes", then I might go so far as to say that the Deligne completeness theorem is a bit of a red herring, drawing as it does attention to the refined condition of coherence, when what is really signficant is the weaker and cruder condition of exponentiability.