Listening to 80-90 B-sides as I type, "Endless Deep" should count too, even without his "vocals".
And agreed that he's literally instrumental to the band. As a bass guitarist myself in an overall-collaborative band, it *matters* to some extent. If I'm not mistaken, he came up for the chord progression for fucking "Pride" (which would make Edge musically subservient, in a sense, for once--a *huge* once).
Some bands "need" all (ideally original members). Joy Division broke up upon Ian Curtis' death because they'd apparently made a pact for Joy Division to only be those four (hence, New Order). U2 (though, musically, seemingly less so for the past half of their existence) "rightfully "need" Adam and Larry--forgetting their (I'd imagine "more-than-considerable") social bond entirely in the context of this post.
That we and the hoi polloi (who obviously know "New Year's Day" and especially "With or Without You" from the get-go, and especially, or perhaps because of, the latter's simplicity), immediately recognize both songs speaks volumes. People may not hear the Eno synth first, or Edge, but as soon as those aforementioned "eighth notes" come in, people both "apprehend" and (maybe) appreciate that they're hearing "With or Without You". It's both mystifyingly simple yet utterly idenitfiiable. (At the very end of U2's and/or Adam's life, that bassline is not only what will always be remembered and cherished, it's the part of a U2 song that I'm willing to bet your "man-on-the-street" will reliably perceive as U2 and/or "With or Without You"--as it kinda is even now!). I'm not sure off the top of my head how many other bands have such a simultaneously simple/immediately-distinctive bassline, maybe I'm forgetting other good examples. Still hard to beat here, especially as a US #1 (not that that "matters", but it's the reason everyone aged 20-70 knows it, at least in passing).
Outside of pure musicality, let's also not forget his early commitment to, and belief in the band, at times when even I believe Bono and Edge weren't sure (and I don't just mean the October-era "crisis").
From my opinion, as a bassist and someone who has been in bands, he is a *great* bandmate--doesn't (at all) have to be musical leader, but someone who is totally devoted to the cause and [should be] truly embraced on all levels.
Also, "while we're at it": "Endless Deep" and "Wire".