Studio songs are just that: studio. By this, I mean that songs we hear on albums are the results of MANY takes and subjected to studio "magic".
If you can, listen to the CD single for "Pride". The CD single version has an extra insert of the chorus. But this extra chorus verse was not subjected to studio tampering - it's Bono raw. And as a result, the vocal is hoarse and not quite as powerful. Sure, Bono still hits the notes, but it's not like the rest of the song.
And this is true for any singer. In the studio, a singer can re-do that missed note, or hoarse voice, or falsetto or whatever.
In concert, though, note that Bono has never sung "Pride" the way he does on UF - not even in the UF tour. It would be nearly impossible for him to belt out those notes night after night.
So to say that Bono couldn't sing some of these songs live isn't really accurate, because he rarely sings as he does on an album. And this was true even in the "glory days" (if you will) of his voice. Bono did not scream out "God Part II" night after night on the LoveTown tour, not like he does on the album. He does not do hit the same notes in the operatic wailing near the end of WoWY in concert as he does on the album.
Now, there are a few times when I thought a concert performance was better than the album - where Bono truly outshined his album vocal performances. But to do this every night would really ruin his voice. Far better for him to leave his vocal acrobats to the album than to ruin them in a one shot concert performance where most fans can't hear him that clearly anyway.