Do caster out of combat options matter?

[Aimeryan]

Two different axis to cater to here: Capability and Agency.

Capability

Here you essentially have three types of DM: ones that will only present challenges the party can handle, ones that will present challenges regardless of capability but will always include a backdoor that the party can handle, ones that will present challenges regardless of capability including the possibility of failing something in the campaign.

In the first, yeah it doesn't really matter what the players can do - they'll always be capable of handling the situation.
In the second, it can matter what the party can do; it may save time, or provide better rewards/no losses, if they can handle the challenge in the more difficult way. Alternatively, it may make no difference - it depends on how the DM handles the players having to use the backdoor.
In the third, it definitely matters what the party can do; whole plotlines, rewards, etc., may be lost otherwise.

So, caster's out of combat options can be very impactful here - but also may not be, depending on the DM.

Agency

With this, it really depends on the player. Some players are just there for the story and could not care less what their character is capable of - it is essentially no different to listening to a non-interactive story in this case. Other players want a game, and so their agency is highly relational to their prospects for fun - afterall, probably the biggest benefit of a tabletop RPG with a human DM is that there can truly be no railroading if desired.

So, caster's out of combat options can be very impactful here - but also may not be, depending on the player.