The idea that a Paly or a monk needs all these high stats is pure BS simply because the player is too lazy to think of a concept of the class or the role of the character. Are you playing a character with weakness and faults or are you playing a wanna be godling that is in mortal form.
You may not want to be a godling in mortal form, but you may still want to be a mechanically effective character.
If character concept and role were all that mattered at all, we wouldnt need any mechanics...and we wouldnt be playing a role playing game, we'd be acting.
Some classes do use and therefore need deccent scores in more stats than others, in order to function fully (or at least remotely well) as a member of their class.
A Wizard for instance could have a 16 Int, a 10 in Wis, Dex, Con and 8's in Str and Cha and still function perfectly well as a wizard (although be at somewhat of a disadvantage as a character overall since the game does assume one will probably have higher stats than that).
However, a paladin, or monk, or bard or ranger with a 16 and even all 10s and no 8s would be unable to really fully function as a member of his class. Or rather, some of his class abilities and functions would do him little or no good.
Even a fighter or barbarian or rogue with such stats would have a hard time.
To be competitive, a paladin needs Cha, Str, Con and Wis. Str and Con for combat, Cha for virtually all his class abilities, and Wis for spells. Now he doesnt need to worry much about save DCs, but still needs at least a 14 to access his best spells.
A ranger needs Str, Dex, Con and Wis. Str, Dex and Con for combat and skills. Wis is probably a touch more important for the Ranger since many of his key skills and his tracking, as well as spells are based on Wis.
A Bard needs Cha, Int, Dex at the minimum..Cha for spells, class abilities, and many skills, Int for Bardic Knowledge, skills and skill points and Dex for skills and defense. If you want to try and use any of what combat ability the bard has you might need a little Str too.
A Monk needs Str, Con, Dex and Wis the first three for combat, and Wis for combat and essentially all class abilities.
Even a Fighter really needs both Str and Con, and for feat purposes is well served to have at least a 13 in Int and Dex. Other specifics will vary depending on what combat style(s) you want to persue. Likewise, a Rogue needs Dex, and Int for sure, and could really use a bit of Str as well.
Now of course as time goes on and levels are gained boosting abilities isnt to terribly hard. However, its still easiest for the more or less total casters...all they really need to do is mostly put their increases in, and get the best item they can for, their casting stat. Its a bit harder for a class like a paladin who not only needs 3 or 4 stats but needs at least a couple of them to increase to continue to be useful.
I'm not entirely sure what the point or context of the question is. But some classes do need mid or high scores in more abilities than others. In a stat-restrictive campaign, like a low-point point buy or one where ability increasing items are rare, paladins, bards, rangers, monks would certainlly be penalized/effected by it more so than other classes. At the other end, the prime casters would be least effected.