Correct. The role for a rogue is exploration expert/scout. The class amplifies the role through it's abilities such that the wizard cannot match it. The same with the paladin and combat. And so on.
No it can't, because the wizard has very few class abilities in comparison, and those abilities generally aren't helpful in the various roles. Exceptions exist, like the Scribe's book, but by and large it's just spells, more spells, combat options and how do I modify a spell.
Spells cannot equal or exceed a class that is specialized in a role plus class abilities to enhance that role.
Knock will very rarely be better unless the wizard has some outside help from a party member, magic item or multiclass to allow it to not bring every monster in the area down on the party.
My argument is not that there aren't cases, and often corner cases, where the wizard's spells can be better, but that generally they are not.
No. Those sometimes things you mentioned do not do what the rogue does just as well, because you didn't take into account the other rogue abilities that enhance what the rogue does.
The rogue can unlock doors all day long. The wizard cannot and is going to wreck the party if he even tries because knock generally sucks now. Because of retries the rogue also gets retries on each door, so unlocking is almost as automatic as knock, but much better because no loud noise. Knock sets of traps. Traps that the rogue can find and disarm, and if that fails, will be mitigated through class abilities to do little or no damage. The wizard gets wrecked.
At mid levels the rogue gets reliable talent, which is huge with the large bonuses provided by expertise and bounded accuracies generally low DCs.
Mostly worse, which is why it isn't as good or better.
Yep. Mostly worse there as well.