So the upshot to all this is:
If the DM wants to screw the players over for lacking an Arcana-trained character, then yes, the players are screwed. If the DM doesn't want to screw the players over, then no, they're not screwed.
But there is no rule in the book that requires screwing the players over, nor is there a rule that explicitly forbids it, though it's clear from the above quotes that the rulebook is more on the side of "just give it to them".
In my games, they'll never walk into a room full of garbage and have to guess which bits of junk are magical. They might find three dozen rusty swords and one untarnished, jewel-inlaid sword, and there's no need to even ask if the rusty ones are magical. Or they might find a dozen average quality, bog-standard but perfectly serviceable swords, and one with an inlay as if the blade were circled with vines of ivy, sitting on a velvet cushion on a stand under a spotlight. The haunting voices of an ethereal choir are optional.