Some additional thoughts on how I see the issues and what I'm trying to do to create a desirable outcome.
No system is truly "universal," because some settings would work better in other systems; sometimes they even need a unique system to really do what they do. I think some universal settings work better than others. While I'm not very familiar with the PbtA system, from the way people talk it does well supporting different settings, and is customized for each one. I think that's a commonality of the systems that work well for different settings--a reasonable degree of customization for that setting. Still, even there you aren't going to be able to support every setting and playstyle. A highly narrativist focused system won't work with some settings, just like a highly simulationist setting won't work well with others.
It is also quite a fine line to be able to encompass most of the common ideas people have about a genre/setting, while still having a richly distinct feel. Some of what I'm working on to attempt to create that involves:
A system that is internally flexible to support different playstyles. Specific meta-options can be chosen, either/or overall for a campaign, for an adventure, or for specific characters, skills, and powers. My system is on the light side, so these aren't adding a bunch of crunch. And example might be character creation and advancement. There is no default that says characters start weak. If you want to play archmagi from the get-go, you can. You could also have different levels of power between characters. This is all decided as a group. Also the primary or suggested way of handling character advancement is to do whatever makes sense. Do you want characters to get better between one story and the next? Then they do, by whatever amount you want them to. If not, they don't. My system isn't designed to function as a game. However, since I realize there might be people who really like my system overall, but are uncomfortable with that level of free-form character design, I'll provide some sort of point-buy system customized to work with the sorts of assumptions that people who want point buy want, while staying faithful to the setting I'm focusing on.
A setting that seeks to incorporate the general commonalities amongst lore (not the specifics). You can't easily mimic any particular franchise with these rules, because that isn't the point. What you can do is choose whether vampires have complex social structures or not (and even vary it in different parts of the world). There would be multiple examples of how you can do different things, some of which are compatible, and others of which are mutually exclusive. Brief examples are given for each element, and then at least two examples of how you could put those elements together for an overall world setting. Magi will not be limited with spell points nor a list of known spells. They will have something more akin to Mage: the Ascension, although it will be possible to exhaust oneself in magic, just like in physical exertion. Unlike the highly unique setting of Mage, with mages that feel totally different from common lore about mages, and with things like Paradox, this system will support more traditional feeling magi, including culturally distinct varieties as well as a common magical theme for them to interact under. You can't play everything with that, but if someone coming in with general fantasy experience wants to play a wizard in a modern fantasy setting, my setting should support the iconic ideas they most likely have.
Flavor distinctions that avoid violating common lore, and are as broadly applicable as reasonable, while still allowing for the flexibility I've mentioned. For instance, vampires will be undead. They have literally (even if only momentarily) died, and their bodies are animated by something different than a lifeforce. They aren't a species or a disease. There are some other commonalities all vampires will share. Beyond that, you can make different types of vampires, and you can include multiple types in your world if you so desire.
A lack of one true setting. While I'm shooting for more than a DIY toolset, elements of that are there, since you choose what to implement and how in the setting. I'm never going to publish a single example of anything, because then, regardless of what I say about making it your own, those single examples will become the default assumptions of what the official world looks like. I can however publish multiple highly flavorful examples, neither of which is how the world officially is, because you choose your own world.
None of that is easy. But that doesn't mean it is impossible. And no matter how well done it is, it cannot be a universal system, because there will always be settings (including highly focused modern fantasy) that aren't compatible with it, or will play much better with their own system. I'm actually a fan of both universal systems and unique, setting specific, settings. They each have their charm and function. While my system will be playstyle flexible, it can't be universal because it won't support certain extremes: having its own baseline leaning unavoidably (at least for me) limits its range of flex.
Of the techniques I'm using, one of the most useful ones, contrary to what I had expected, is to start with settings I kind of like, but don't like parts of (such as WoD), and identify what parts I don't like (or thing are highly unique), and what I think would be more traditional. I had originally attempted to start from a blank slate (and I still do in some cases), but after a lot of work eventually realized that it helps tremendously to look at it from a negative perspective (what parts would I take away from setting X), rather than only from a positive (what would I put into my setting). Both are necessary for me.
As I said, none of this is easy, and some parts are going to be easier or harder depending on setting. For instance, the same system also applies to my space opera setting, but the challenges are a bit different, since more things need to be clearly defined to make it functional, and those things may make it too distinctly unique if I'm not very careful.
