I agree with the posters who've said (and/or implied) that the impact of out-of-combat abilities can depend greatly on the style of campaign in question. I see two major ways that usually plays out.

First, the more freedom the players have to set their characters' long-term goals, short-term objectives, and choice of methods, the more likely it is that the presence or absence of out-of-combat abilities will be a significant factor in how the campaign unfolds. Upthread the example was raised of an underwater city. In a game where the DM sets the party's goals, and decides that the goal is to infiltrate the underwater city as part of some intrigue with the mainland, then it's true that knowing Water Breathing is going to be, at best, a time-saver (although see below for how that can still matter). If instead the underwater city and the intrigue with the mainland are part of the campaign world that the players can choose whether, when, and how to engage with, then knowing Water Breathing opens up a lot more options. A party that doesn't have the ability to breathe underwater (or have easy access to allies that can provide that capability) has more constrained choices in how to engage (if at all) with that intrigue, but that's fine--not all options need to be equally available. Indeed, part of the fun of such campaigns is applying your limited resources to solve or bypass the obstacles to accomplishing the goals you've chosen. Maybe such a party tries negotiating with the underwater city, or recruits other underwater factions to oppose the city, or allies with the underwater city, or concludes that the opportunity cost of obtaining the ability to breathe underwater for an infiltration simply isn't worth the time--instead choosing some other goal that their resources are better suited to tackle.

Secondly, the less static the campaign world is, the more likely it is that out-of-combat abilities will be significant. Primarily, that's because such a game world doesn't wait for the PCs, and opportunities or make a difference are often time-limited. Time-saving abilities thus can make goals and objectives achievable that would otherwise be mutually exclusive. Furthermore, in some cases saving time can dramatically increase the PCs' ability to impact a single, large-scale situation. For example, if an enemy nation is invading on multiple fronts, the PCs might ordinarily be able to pick a single axis of advance and thwart it, but can't be everywhere at once, and so the broader invasion continues. With Teleport, the distance/time factor changes radically, and the PCs can indeed impact multiple threat axes. The enemy may not care much if one advance force gets stymied (they simply reinforce an axis where they did break through), but if all their advance forces get stopped that's going to profoundly affect their strategic options and planning. So time-saving out-of-combat abilities can still matter, even in a game where the DM picks the party's goals. Of course, in a more static campaign world where time isn't as much of a factor, time-saving abilities can indeed be more irrelevant.

One last point I'd like to make though is one that hasn't been raised yet. The more an out-of-combat ability can impact how a campaign unfolds, the more that ability becomes a party-level resource, rather than just a character-level one. The Wizard who uses their high-level spells slots to Teleport the party to multiple battlefields in time to make a difference to the outcomes enables the party to be spectacularly more impactful to the war effort, but once that capability is available the whole party gets to participate in figuring out how best to make use of it. The same can be true with other abilities like Fabricate, various divinations, Fly, and a whole host of other abilities. Importantly, that switch from character-level resource to party-level resource has a profound impact on intraparty balance. The Wizard in a party that makes good use of Teleport (in a campaign run in a style where that matters) is providing essential capability, but arguably isn't stealing the show to the same extent they would be if they routinely cast encounter-ending spells in a series of combat encounters. Indeed, in some cases, intraparty balance in such circumstances can disfavor the casters if they (e.g.) feel relegated to the role of taxi. Balance is so inherently subjective that I'm not trying to make any broad conclusions here. I'm just trying to point out that, counter-intuitively, running a campaign in a style that enables out-of-combat abilities to have more impact doesn't necessarily magnify balance concerns between classes that have more such abilities and classes that have fewer.