If PCs are stopping regularly to Refocus and Tend Wounds, having one of them spend some time to Identify Magic is not much of a cost. It only requires being trained, so the party can coordinate who does what to minimize downtime.
Being able to fail the check is a thing, but one could say that of knowledge checks in general. I’d let PCs use a magic item without identifying it when it made sense (such as when activation is part of another activity, like using an unidentified magical sword to Strike a creature), but I’m inclined to keep the check.
Well, not really (and this goes to a core issue I have with PF2).
Either the decision to take ten minutes to recuperate is a meaningful one, and there are consequences for taking it: a risk of wandering monsters, or that the princess gets eaten, or whatever. There is a real cost to taking each 10 minute period, so you want to take as few as possible while still not entering the next fight hobbled by injury.
Or, the decision doesn't matter much, because you have lots of time. Say, one hour here or there doesn't matter much. But in this case -
why have all these little rules, with a myriad of check DCs, modifiers, and effects of actions? Why not simplify away all the decision-making and all the die-rolling and all the cluttery administration with a simple "a couple of hours later, you're all back to maximum hit points" since that's what all dem rules lead to
anyway, you just save a load of playtime for the exact same net result. In short, instead of spending your time checking skill bonuses, making rolls and adding up healing, you could just... skip all that malarkey and go right back to the adventure.
This is relevant since each time the Cleric says "I need to Treat Wounds before I have time to Identify Magic" you end up in this situation. Either your downtime management matters, in which case it sucks that Divine magic items have a much lower rate of identification (in number of items identified per hour) than, say, Occult, which both the Ranger and the Bard are trained in.
But even if the party had distributed their skill proficiencies differently, there's still something inherently dodgy about "whelp, that's a 2 on the die. Guess we'll have to sit around doing nothing for ten more minutes" (if retries are allowed) or even worse, "whelp, that's a 2 on the die. Guess I'll write down 'mystery object #14 on my character sheet' giving me at least a chance of remembering to check it out again once I have leveled up, even though I am fairly certain it's not worth the trouble".
Or, your downtime doesn't matter, and you'd be a fool to roll the dice instead of just having the GM say "it's a [insert item name and CRB page number here]" and get on with what's actually fun: adventuring!