Not by a long shot. Unless you have something like an Elise or a super car that don't come with 6 in wide wheels and tires from the factory, there is always room for plenty of improvement.
There is... but improvements have to be made all-together... not just by slapping bigger wheels and wider tires without any other changes.
Wider and lighter wheels with tires will allow you to fit a better tire. I really don't want to get into the advantages of having a much lighter wheel and a wider and more "adhesive" tire compound as I'm sure everyone here is competent enough to understand them.
True.

Maybe you were unable to properly transfer your thoughts on to the keyboard due to being sleepy/tired. I'll give you the benefit of the doubt. But how in the world do you manage to fit a tire from one size wheel (both in diameter and width) to another one? Even if the other wheel was the same diameter but just wider, you'd still be stretching a stock tire, not making the contact patch any wider. Then as you said, pump it up to "prevent" sidewall deformation? To what? 40 psi
I meant what I said. Go up a size, down in profile and fit the exact same model and tire compound (ergo: from crappy Eagle 205-55-16 NCT5s to bigger 205-50-17 Eagle NCT5s) and you get bumpkis in handling improvement... or merely the same improvement you'd get from pumping up the old tires to prevent sidewall deformation. Granted, if the tire is much wider, it will take longer to overheat, but over a single lap, there won't be much advantage in that.
The proliferation of "tuner" tires... i.e.: tires in low-profile and wide sizes in the same compound as smaller tires... is a good example of how bigger (and sometimes, wider), by itself, isn't better. At times, I've driven cars on low-pros that handled worse than stock on the racetrack... simply because the extra weight of the wheel-tire combo wasn't balanced with better grip from the tire. You know stock is enough when you're outcornering a Cooper S on 17" wheels in a Cooper on 15" wheels simply because you're wearing similar tire compounds and your higher profiles not only give you the same grip (and a more predictable edge of adhesion), but allow you to jump kerbs more easily.

Even without kerb-jumping... there was no difference in mid-corner pace.
*obviously... this isn't the stock compound for either... as the Bridgestones on the Cooper S are undoubtedly superior to the 15" Contisports... but a third tire that was used for this trackday because it was cheap and disposable...

).
A better compound, however, is always good... and I'll grant you that you can often find better tires in wider, low-profile sizes.
Wider wheels only effect your scrub radius when their offset is the same as the narrower wheel. And the scrub radius changing is detrimental to performance in the sense of feel, not actual cornering speeds. And I mean "feel" as in, like in my car (NA Miata,) where road imperfections will tend to pull the wheels to follow them. Keep in mind this is with no power steering, 320mm Momo steering wheel, and R888s (I have 15x7 +20 offset Weds.) When I ever go driving on roads outside the city this doesn't happen. Not that it is ever much of a problem through the uneven road through town anyways.
I'll debate whether it's "merely feel" if the steering becomes more sensitive to bumps and cambers... and when you go past a certain width, the radius will change if you can't package the wheel any closer to the suspension on the inboard side. Probably not a big issue with your Miata, but with strut suspension cars, it's a biggie. Of course... I agree that you can run maybe 10-20mm extra width with no problems.
In racing the best wheels are the smallest you can fit around the brakes and the widest necessary to fit the widest tires allowed by the regulations. You're confusing association with causation. Getting wider tires wont change the scrub radius. Changing the wheels offset, and thus its distance relative to any point in the cars body, will.
I'll give you that much.
Getting a one or two inch larger wheel in diameter compared to stock is usually the way to go (depending on the car.) It will allow you to fit a better tire size (lower profile) and larger brakes. Logically, getting the widest wheel you could conveniently fit to allow for a wider tire without having to stretch is the way to go. Then you chose an offset that will allow for a flush fitment.
Typically, yes. Depending on the car (as you say). If the car already has incredibly large-diameter wheels with rubber-band tires, you aren't gaining anything by dropping from a 50 profile down to 40 or even 35. In fact, you're probably losing a lot of the compliance needed to "kiss the curbs" on a racetrack... or survive brushes with them on the road.

...and even then. I seem to recall one Top Gear Australia episode where they showed that the ultra-thin tires and big wheels on a factory-special Holden made it slower around the track than if they'd left it on the stock options (which were an already big 17" or 18" set)...
Also, most race car's wheels have very low offset and it is very unlikely the engineers design anything into the suspension geometry to account for the steering effect since it's simply not significant enough in a car with power steering (or even my car without it.) Cars such as in BTCC/WTCC all have relatively low offset wheels all to clear the calipers. The same is true in WRC cars with the wheels they use for tarmac.
But those cars are designed around them.
Let me mention I'm also fully aware that, more often than not, a wider and slightly larger in diameter wheel (although by itself can be lighter than stock) will be heavier due to the larger tires. Nevertheless the benefits will outweigh the disadvantages, given a good, lightweight wheel.
To note: You can also get a good (even lighter) lightweight wheel in small sizes with the width to fit big tires. I flirted briefly with larger wheels, then found that performance overall was better with the same width of tire on stock diameter wheels (since I didn't need anything taller to fit over my new brakes).... because the combo was lighter, with the same amount of grip available.
And like HFS says... it rides infinitely better. I got sharper turn-in with a lower profile... but I found that pumping up the pressures for those times when I'd actually need it allowed me to have both pothole-survival/ride comfort and outright performance in the same package.
As HFS notes: our roads are almost British in some places.
Unless you've driven down a road 15 miles from anywhere with potholes as large as the car itsself, I may not believe you.
I once hit a brand new one... six inches deep on a perfectly flat and level highway... where a typhoon and the passage of trucks ripped out a chunk of concrete leaving a hole with nice sharp edges.
Didn't see it at all, as it was perfectly flush, and it was raining. Hit it at sixty (mph... 100 km/h!) and it pushed my rim out of shape by about half an inch. And that was with stock diameter wheels. People riding on low-pros (40-aspect ratio and below) sometimes get cracked wheels from the roads around here.