Currently, that "one encounter" of four floors is the ENTIRE endgame for anyone who raids seriously in content that requires a Static group rather than just DF/PF. Yes, a small portion of the playerbase do this content but that's the portion that are complaining on the forums. Right now many dedicated paladins have felt the need to be forced to swap main because their group likely wouldn't be able handle the content until much better geared unless they swapped. Just because not everyone does this aspect of the game doesnt mean the class shouldn't be fixed.
It's worth mentioning that at the last census, something like over 35,000 players had killed Alex 2 Savage. 35,000 players is a -significant- number that care about balance. Was closer to 100,000 or so actually participating in Alex 1 Savage onwards.
Also, yes paladin is viable in all other areas of the game, but it still suffers from one issue once you reach 60 - it does noticeably less DPS than the other tanks, and its advantage of "a tiny bit more mitigation" is basically irrelevant. The difference isnt as noticeable because bringing a Paladin isnt going to mean you flat out fail a dps check and wipe, but in the easier content Paladin can still benefit from some threat/quality of life changes to bring it up to par.
Basically you're right - the reason Paladin is bad now is due to the current tanking meta that says that tanks are capable of tanking content in low vitality Slaying accessories whilst spending most of their time tanking in DPS stance (thus rendering most of their mitigation power kind of irrelevant as it mostly just forces the burden onto the healers and means tanking has turned into "hold threat, DPS as hard as possible and pop a cooldown for a tankbuster"). Couple this with most of the difficulty coming from incredibly harsh DPS checks and right now tanks are basically a DPS class that has to press a cooldown at certain points in an encounter. Until the tank meta changes significantly paladins will always be the least desired tank, and the difference in potential dps between a paladin and a warrior right now -is- the difference between some groups (or current groups before they got more gear) literally not being able to kill a fight.
Also it's worth mentioning that whilst Paladins are -able- to complete at least the first 3 floors of Alex Savage right now, this is now at the point where people are starting to get overgeared from the original tuning intention. Once you overgear a fight then quibbling over balance issues is kind of irrelevant because good static groups start messing around with all sorts of weird lineups like 7 tanks 1 healer for giggles.
It's a fine balance between classes at the top end raiding. The objective isnt for all classes to feel the same, or equally strong, it's to feel that each class brings enough Advantages to the table that any Disadvantages they show are countered for the most part, and thus every class is viable in cutting edge content. Some classes might make a specific encounter easier, but these should even out across encounters.
Right now the issue is simply that for all the encounters in Alex Savage with the tank meta as it is, Paladin is the objectively worst tank on pretty much all four floors (A2S notwithstanding if your group has enough AOE without it). Right now, not a single group has killed A4S with a paladin. It's not that they're slightly worse in some situations, it's that their kit renders a lot of fights simply impossible to do until a group is overgeared, or at least makes an encounter a lot harder.
Because raiders don't want to hold their static back, a lot of paladins have chosen to swap main to Warrior or Dark Knight (not an easy feat with the way esoterics restrict gear to one class). That's a sign that paladin needs something to bring them up to spec - and it's worth noting that the things that paladins really -need- to perform (increased threat, higher single target damage in tank stance but not sword oath, definitely not any increased mitigation) wont be massive boosts outside of Alex Savage other than making 4mans a little easier on the paladin.