I know that native distortion of m43 wide angles is generally terrible. 6% or more is common, which is a huge amount of distortion. This often results in soft corners when correction is applied.
What do you mean by often and by soft? Because I am pretty sure I could post corrected and uncorrected corner crops from my 12-100 for example and you will not be able to tell the difference. Althought I am sure you could measure the difference.
That may well be the case with that specific lens but it is most certainly not the case with the 7-14mm pro or 12-40mm pro or many other m43 lenses
No, they are all in the same ballpark, which is more than 6%. The 7-14 at 7 mm is the most extreme example, as it has probably one of the highest distortions among MFT lenses, at a whooping 8%. That's even more than Canon's 11-24 mm f/4L with its 7.3%.
So, if you compare correctly, it is a very different story.
I am, and it isn’t. But if you have a different idea of what comparing correctly is, I’m opened for duscussion. For me, the „correct” way to compare is to look at uncorrected raw files.
A FF lens truly equivalent to the Panasonic 12mm F/1.4 is a 24mm F/2.8
There are very little lenses like that. But the ones that do exist are equally bad or even worse than their f/1.4 cousins. Samyang 24mm f/2.8 even at F8 looses more light than PL 12 wide open. Canon 24mm f/2.8 is a lot better, it matches wide open PanaLeica already at f/4. A similar story with Batis 25mm f/2. All of them are noticeably worse at f/2.8.
, a FF 24mm F/1.4 is equivalent to a m43 12mm F/0.7. But lest ignore that for a second, wide angle mirrorless lenses , tend to apply more software corrections than less wide lenses.
That's understandable and is true for all lenses from all brands and systems. The wider the lens, the harder it is to correct it optically. Same goes for zooms, especially ones with high zoom ratios.
And while I can understand complaints about prime lenses showing serious geometric distortion, the same complaints about UWA zooms seem a bit iffy. Because distortion in the 4-6% range is normal for lenses like that, regardless of the system, format or who makes them. There are not many UWA zooms that do not show significant distortion at the wide end.
Whilst Sony applies some,notably vignette correction where they sometimes let it go very high, which I complain about in the Sony forum, with much the same response I get from the diehards here

with regard to distortion and the like no one is correcting on the scale of m43 .
That's true. But what practical effect does it have on image quality?
The complaint is that it makes corners soft. But I never saw that demonstrated and my experiments do not support this claim either. I'm sure you can measure it using a test chart, but I'm equally sure you could not tell them apart visually on an actual photo. A "natural" corner softness will still be the dominant factor here.
And if you gave me a choice between the two, I'll take distortion over vignetting. The hardware pinhole effect is cute and all, but gets very old very fast. And raising corners by 3 or 4 stops when doing astro for example, has much more dramatic negative impact on final image than correcting 6% barrel distortion.
Here is the Panasonic 12mm F/1.4 compared corrected and uncorrected at F/1.4 vs the new Sony 24mm F/1.4 also at F/1.4 . Using RAW samples from DPreview sample galleries
12mm F/1.4 the bright area highlighted in this corner crop is the are sacrificed to software.
Sony 24mm F/1.4 at F/1.4 corner crop of corrected and uncorrected
I appreciate the illustrations, but even your example does not show corner softening. At least I cannot see it there.
Also, the degree of "loss" depends on what software you use.
Here's my demonstration .