On the bright side, it would be relatively (but not trivially) easy to play without level to proficiency:
Try subtracting you level from each and every check, attack and save you make (including AC, Perception and static skill DCs).
Mathematically this is true. Producing a quality gaming result is another matter altogether.
PF2E is designed from the ground up with the presumption of this +level factor built in. Yes, you get D20+X compared to DC = Y and you can do the math. But (IMO) a good storytelling mechanical foundation should make sense in terms of how various checks compare to each other. As written PF2E modifiers are frequently on the order of 50% dominated by level (at least after the first few levels). Backing that out across the board from a system which relied on the presumption of +level creates a semi-random outcome.
The whole four tiers (+/- 10) feature gets particularly wacky. But that is not the only concern.
And I'm sure someone will ignore this and quote me wildly out of context, but if someone doesn't care a hill of beans about how the mechanics are self consistent in this way, then my comments won't apply to them.
The result should resemble 5E quite a bit, seeing that without level the proficiency bonus ranges from +2 to +8, quite similar to how it goes from +2 to +6 in 5E.
I don't think this is at all true beyond the most trivial of elements. Just as PF2E was designed with +level as a fundamental presumption, 5E was designed knowing that bounded accuracy was its foundation. The huge distinction is baked in throughout little details of everything.
Obviously I can't comment on what Paizo is going to publish. But it will need to be a really sophisticated retooling to be a solid alternative.
The standard for a really good TTRPG is very high. People have a lot of choices and fans with different preferences can be choose a game that caters to them. As lot of companies have demonstrated, simply publishing a game that "works" is easy. That doesn't go very far.
There are a lot of PF2E fans who love the +level system. It seems reasonable to assume that most of them want to keep +level and won't see this alternative as an improvement. Why should they? It is removing a feature.
By the same token, it will be hard to sell someone who doesn't like +level on a +level system with that feature backed out when they have great alternatives which are not based in any way on +level.
Again, no idea what Paizo is doing. We shall see.
But as to simply taking the game "as is" and backing out level, this does not produce something comparable to 5E.