I think you expected too much...
1. Older airports that cannot cope with the traffic levels have these type of restrictions. QF at SYD/MEL International Terminals will not check you in more than 4 hours prior to departure. DOH is a new airport with fully automated baggage system, so it does not have these restrictions. I guess a new AUH Midfield Terminal that should be inaugurated soon will not have these restrictions, either.
2. EY now has a very few aircraft with F - was there any F-class departure even scheduled when you tried to check-in? If not I am fairly sure they assumed you are a Platinum member using F-class check-in. If memory serves in DOH true First Class passengers are segregated from Emeralds not traveling in F - in AUH First Class is mixed up with Platinums. But it is not much different from may oneWorld carriers that also mix up First with Emeralds (again - QF comes to mind).