Arcaneum definitely should sell a Primed version of every item. It's especially strange that there is no Primed longsword for sale. Also maybe Loremaster should be able to craft things without needing a Primed item. It would still be worse than the other two choices for Wizard but its at least something. Two of my three parties have no primed chain shirt and one primed longsword...the third one has the shirt and 3 longswords.
And yeah I think they should sell all the item ingredients somewhere.
IMO Antiquarian is clearly OP right now. All the +2 books and the +STR gear not to mention Cloak of Elvenkind, shoes that give spider climb that don't need to be attuned, +19 INT hat, Cloak of Protection, etc. Definitely the best faction IMO.
With respect to faction rep, no EA experience here but I have started 3 parties with the release version and they are level 7 9 and 10 parties, so pretty deep into the game with all three. My first party I definitely missed some faction items and also sold them willy nilly to whoever I happened to be talking to thinking that I'd get to max with all of them eventually. My second and third parties I was much more careful and my strategy was to rush Antiquarian to Living Legend (81+) for the +25 STR belt and then level up Arcaneum and Danatar at roughly the same pace since both of them have very solid Alliance and Brotherhood items. Tower is crap but if you just say hi to the lady every time you are in town you get 4 faction so you can hit LL easy with that one.
Anyway. I am able to get LL with Antiquarian after the Monastery Gem quest around level 6-7. At level 9 I am Brotherhood with both Arcaneum and Danatar and still have at least 2 side quests and 1 gem quest left. So it might be possible to get LL with all the factions if you don't miss any faction items/choices...we shall see.