They have a mechanical effect, but so do attributes, feats and equipment. Everything should be noted on the character sheet, but that doesn't mean that you mention it in the same breath as race and class. You say it's unwieldy to say to mention race, class, theme and background as "full title" . . . under what kind of circumstance would you ever need to?
There are various instances when I figure I might need to reference it:
1. I know I'm probably the minority in this, but I repeat the names/classes/titles of creatures in my head our out loud while building an encounter - particularly relevant things. Sometimes I call them "names" that don't mean anything mechanically like "dervish" that might actually be useful in 5e - that means that I'd like to be able to call an orc dervish exactly that and have an idea of what it means in my mind. Fighter means something to me, so if themes and backgrounds are simple and easy to remember and easy to say together (or they imply other aspects of a character), then I'll be pleased.
2. Many times my players will ask if an NPC looks like a member of a certain class. If theme and background play any kind of significant role in the game then I suspect they'll ask about those as well. So a player might ask "does this guy look like a fighter?" and I'd say "you might guess so, based on his arms and armor. Doesn't look like a magic user, at least. He's painted in tribal dyes and designs all over his body and wears leather armor. In his half-opened backpack on the ground you think you can see a variety of potions and sensitive instruments that you'd guess are related to potion-making." and then the player might ask "how tough does he look" and I might respond "he looks a little bit tougher than you". The player might then respond "okay, guys, I think this person is a lvl 5 or 6 half-orc fighter-berserker-alchemist." Which just feels awkward compared to someone saying "looks like a level 5 or 6 half-orc barbarian, with alchemy skills".
3. I give a lot of DM's I know advice on encounter building, so I might say "I'd throw a lvl 6 half-elf sorc with two level 4 human barbarian guards and say...eight level 1 human fighter minions", which is way easier to say in a phone call than "I'd throw a lvl 6 half-elf sorc-blood mage-arcanist, two level 4 human fighter-berserker-trackers, and eight level 1 human fighter-slayer-commoners."
Does that make sense? Say "level 6 Paladin" and you immediately have a snapshot of what that means, whereas the same statement in 5e might be much more ambiguous when background and theme come into play. It would be convenient if certain combinations had a shorthand reference and if their effects were easy to remember. It particularly helps if the names are very evocative, simple, and memorable.
I wasn't actually arguing against this point at all. But in general I would guess that there's two questions here. For quick NPCs do you need to fully create a character? For quick NPCs that ARE full characters, do you need to switch from the default theme and background assumptions? It might be easy to remember what a fighter/slayer/soldier looks like (or at least as easy as it is to remember what a previous edition fighter looks like), and you only bust out the customization options on NPCs you want to be special, unusual, or memorable. And then, yes, you spend a little more time making that NPC.
I know you weren't arguing the point, I was trying to explain a portion of my reasoning - since I prefer to DM on-the-fly, I'd like it if themes and background are either easy to remember and apply when I need them or if they just aren't necessary to challenge the party with an NPC/encounter.
Ultimately, these aren't concerns in the sense of "I think 5e is doing this wrong!" but rather in the sense of "I'm wondering about these issues and if the designers are taking steps to deal with them." These are really just my thoughts/concerns regarding the whole topic but I'm nowhere near panic mode on the issue yet. I'll wait to see the playtest to form a solid opinion.