We should be able to see item details for the daily reward.
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You're talking about items from a Chest, not Daily Rewards.
I agree with you, I think it would be a good idea to provide at least tier and quality info on the screen so you can make a better decision when finding items in chests.
From experience and from discussions with others, items from Chests are generally only poor or good quality like the Equipment shop, at least in Common and Unique chests so far. No idea if the item quality improves in higher level chests because we can't really get Exploration to that level under the current circumstances.
Rare chest items are poor and good, also each tier of items look different so you need to learn what the equipment looks like and then you will know what it is.
Also from my experience Common chest have Tier 1 & Tier 2 items, Unique have Tier 3 & 4, and Rare have Tier 5 & 6 so would guess the next lot of chest would have 7-8 and 9-10 in them.