SPOILERISH
Maybe I'm missing something, but there seems to be no purpose behind getting made an "official" wizard. The Wizkid wallet wasn't needed at all. Do you need that official title in addition to the spell book before your magic words work in the duel?

you need to become a wizard in order to fight against the witch

I've not played enough of the game to know the issue here, but...
Adventure game have a habit of including seeming useless items. Either as a red herring or to allow about of humour based discussion between characters.
Some items you just need to possess in order to advance the story, but have no interactivity.

It's been years and years since I played this game, but IIRC the matches do come useful at the end. ;)

SPOILERS
IIRC those are the souvenir matches taken off the counter near the fiery pit. Those matches in the bar are really useless I think.

I think those are there in case you don't pick up the ones in the bar.

Don't you lose everything but the postcard (for obvious reasons) in your inventory when teleporting to the Fiery Pits?

Huh, maybe you're right. It's been such a long time, I just don't remember. But hey, I bought the damn thing off of here, I might actually play it and find out. :D

The matches from the tavern are, as far as I can tell upon recently finishing the game, useless. The same can be said of the placard, taken from the troll.
Also, has anyone found a use for the fruit machine? I tried using a gold piece on it, only to be told that he learned his lesson, as if the character had tried his luck previously.

I think if you don't have the matches from in the tavern you can't smoke out the bees and get the wax and then get the beer barrel for the dwarf. I think all the puzzles in this game were really well thought out and came together quite well. My biggest gripe was the useless hot spots or red herrings. But, there were only a few.

Yep, you need the matches from the tavern to use in the smoke box. If you have them in your inventory when you get to that point though, it's not made obvious (the player doesn't interact with them). But if you don't have them Simon says something along the lines of "I've got nothing to light the smoke box with".
I don't recall there being any "needless" puzzles as such. I've played the game from beginning to end quite a few times now and I'm pretty sure every puzzle has a useful outcome.
That fruit machine is definitely a red herring though. When I first played the game I remember puzzling over it for ages. XD

There are also useless locations, such as the stone table in the forest :)

I think they made it so you could go to the stone table so that it didn't seem like the opening scenes happened somewhere else. That was a nice touch, but it was also a bit irritating cause I'd keep thinking they'd serve a purpose later, only to find out they didn't.