Here we go....
- Are there any ILC cameras with kit lenses (not necessarily telephotos) that are really good?
Yes.
Or are they all placeholders until the user can afford to buy decent lenses?
No.
- Do ILC cameras "know" which lens is attached and apply any software tweaks based on which lens is fixed to the camera at the time?
Usually, yes.
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I am not trying be cheeky. You asked specific questions, those are specific answers.
With that out of the way, I wonder if, with regards to the first and second question, are you actually looking for examples (like the oft cited Fuji in the comments) to prove the point or are you looking for a specific recommendation. In either case (and again, as others have posted), it's hard to respond without knowing what you mean by decent. Are you seeking MTF or DXO style bench testing numbers; aperture size and design that allows not only the creation of bokeh, but pleasing bokeh; high magnification (in the face of macro/micro market speak) at some useful focal length (i,e, short tele or longer); step-less/click-less silent aperture and silent zooming for video; bright, large f-stop for low light-size be damned or size in proportion the ILC/ML bodies with an okay f stop; zoom vs prime (i.e. Fuji zoom vs EOS M 22 prime--both well regarded); or a general lens that does everything okay and has no glaring faults.
Going with the general lens that does everything okay and has no glaring faults is what you mean by decent and assuming that you're not looking at any of the hi-res sensors (greater than 16MP) or the Sony FF mirrorless, I think that most of what you find on the market today is probably better that the non-IS/VR DSLR kit lenses on entry level DSLRs. When you look at the twin lens kits, I think it's almost certainly true.
When I am asked this question by people who are buying a new camera my response is usually, "Hey, the kit lens only adds $XX (usually not much for ILC/ML) to the price, if you don't like it you can upgrade later and if you wait for a lens sale, you'll probably be better off financially. After all, you may decide you don't even like the ILC/ML camera, regardless of lens." I say this knowing most photographers limitations (especially beginners or frequent camera switchers) have nothing to do with the lens and their pictures won't really look better with a more expensive lens until they really fine tune their technique. Most lenses are spectacularly better on digital sensors with software correction than anything you could afford 15-20 years ago and they were taking great photos then too. You of course, may not be in that group and I don't mean to place you there. But for those who are, practice and a couple of classes (good classes) are a better investment when buying a new camera.
With regard to your last question about software correction applied by the camera because it knows the lens, this is an area where opinions rage. Here is mine.
First, lens corrections via software for OOC jpgs is common across the board, whether mirror or mirrorless. It's pretty much a given in m4/3 and really common in APS-C ILC/ML cameras. It's WAY cheaper to design a good lens and make it better via software correction than it is to make a better lens optically. So you get a better lens output at lower cost.
Second, lens corrections via software can be baked into RAW files too. Lightroom and Adobe Camera Raw (and other some other RAW processors) tend to recognise that by default (and it's why many camera/lens combos don't seem to have a lens correction listed--because LR and ACR are using the lens correction data embedded in the RAW file. However if you run the same RAW file through some other RAW processors that don't use the embedded software correction, then bingo--you get distortion, chromatic aberration and other issues that the software in the camera would normally take care of. You now get to do it by hand.
Third, the user world breaks out into several groups on in-camera lens software corrections.
Those who don't even know or care that it is happening.
Those who know and are happy that lens performance is improved.
Those who are intensely angry that the lens maker is tricking them by giving them better performance than the lens is capable of with software correction.
Those who are intensely angry that the lens imperfections are corrected in the RAW file, as this is somehow impure.
Note that people can be in both group 3 & 4 at the same time.
As you can guess, I am in group 2.
So overall, despite my ponderous reply, here is my bottom line to the overarching issue in the OP.
ML bridge cameras with largish sensors may often come with a better lens (especially after software correction) than the kit lenses in DSLR kits. In many picture taking situations they can rival or exceed the results you get with a DSLR that has a dodgy kit lens (not all do). In other picture taking situations--even with the dodgy kit lens--the DSLR will win out.
ILC camera kit lenses (with a couple of notable exceptions) are not place holder lenses--as compared to DSLRs bundled with dodgy kit lenses (which doesn't mean all DSLR kit lenses, and it's mostly at the lower end, entry level where the kit lenses can be bad).
Most photographers (not necessarily most photographers here in PL/SC) need to up their game to the level of their kit lens before they worry about their glass.
Cheers JSD
Oh, Here's a low res sample from an RX100--I did not feel limited by the lens, but may have been if it had been an entry level DSLR with a dodgy kit lens.