First off, a short summary, since this campaign world is perhaps less known to recent gamers:
- player characters (and some NPCs) are special, more special than normal, having bloodline powers.
- Iconic monsters like "The Spider" or "The Werewolf" are leaders of their own countries. That's not a Spider, it's the Spider, a powerful monster-king with plans of his own. The term is "awnsheghlien", meaning someone given great dark powers by twisted corruption. Basically, it could be you except you got vampire powers and became really powerful and evil, and took the name "The Vampire", reshaping an entire country to match your mood. It's a bit like Highlander in that you kill other powerful leaders and take their power (and hope it doesn't corrupt you).
- the campaign world supports domain-level play, where bloodline characters are leaders of their chosen nation and generate regency points, of which there are four kinds, one for each of the four base classes: law (fighters), temple (clerics), source (wizards) and guild (rogues). Points can then be used to raise armies, cast mighty spells, and develop your country's provinces. There is an economic map with loads of provinces, and conquering a rich province can be a goal in itself for players, or just a necessary stepping-stone in order to be able to defend the borders against the Spider's marauding troops...
- the world Cerilia consists of many nations, grouped in five broad ethnic groups. So you'll have all the faux medieval Europe nations here, all the rugged mountaneous Scandi-Slavic nations over there, the desert people with their magical cities somewhere else. Sprinkled in among these are your stock elf forest kingdoms, your dwarf underground kingdoms, and... the Gorgon and its country there, the Sphinx and her country over there.
What would a 5E version look like?
Basically what's cool about the setting is the notion that iconic monsters have risen to become leaders of their own distinct countries, and that there is support for what happens when that iconic monster raises an army to invade your home country. That's what sets Birthright apart imo.
The actual world is pretty samey, with lots of indistinguishable versions of western kingdoms here, several Arabic nations there, and so on. It's so large and interchangeable. And it's obviously in need of a stereotype cleanup. Basically, the question needs to be asked: would 5E be better served by a new much "tighter" map, where you start with the idea to focus on one corner of the world (with maybe 20 nations), but then make sure to include real diversity (and not just 20 different faux-scandinavian forested independent-but-proud nations), cutting out the chaff. Only include as many nations as you're able to make feel different! A new map, a new world but with the core ideas of the old AD&D setting.
As for bloodlines I definitely feel the 5E way would be to simply say that any player character is by default a special person. No cluttery bloodlines powers needed or wanted. If you don't have regency, you're a NPC. Simple. In AD&D it was already very common to simulate a living breathing campaign world by giving NPCs class levels. You would discuss how many level 7 fighters or level 4 paladins etc a given city could support, for instance. Thus it was felt heroes with bloodlines needed extra bloodline powers to elevate them above "regular level 7 fighters". Since 5E doesn't work that way (which is great), I suggest simply that what in other campaign worlds is a "regular hero" in Birthright is a special hero. Same stats, no extra rules.
As for the domain layer of play, I have a sneaking suspicion the numbers were basically just made up. It was enough to support a GMs hand-holding but nothing that stood up against real scrutiny. Compare to a board game. A board game needs to be balanced in some sense. Its numbers can't just be made up or there is no challenge. Most economic tidbits in rpgs just doesn't work. Either it's trivial to get rich or you would bankrupt your organization as soon as you tried gaming out the rules. I suspect this layer could benefit the most from getting a brand new do-over, assuming its developers are given enough time to actually get it right.
In summary:
Cerilia as a game world is a bit naff and the cool ideas of Birthright would probably be better served by a new map. The things I would get a 5E Birthright module for is the economic overlay, and the old one is probably not worth using as a starting point. The other thing I want is the cool monster kings - and their nations - and of course: adventure material that marries regular adventuring with domain-level rewards. After all, you're gaming in Birthright because hunting down that beast or finding out who's poisoning your village well is part of a greater whole. You don't just do it because you're sell-swords, you're doing it because the beast hinders development of your province or chokes an important trade route, and the poisoned wells is a sabotage campaign by raiders from the neighboring country...