I think with this information – that checking everyone’s collection every day is maybe a disproportionate server strain – it could be reasonable to work with the system and understand that sometimes it doesn’t quite offer something that actually helps.
In terms of “Bronze Elite Level 5 Troops” → Common troop offer, I can see how you need to have troops fully ascended and levelled etc. before you can Medal them as part of a potential roadblock which would be included in the offers, and I can also see how this particular task could be tweaked/improved to specifically offer Medals instead, given that to reach this Task you probably already have a fair few troops maxed out.
I could be reading it wrong, but I’m thinking the only case in which the second Daily Offer would have the potential to be an Imperial Deed is if all achievable Kingdom Power tasks are completed or if one of those Tasks requires an Imperial Deed (e.g. “Upgrade a Kingdom to Level 16” at Power Level 24 – currently out of reach).