And it is impossible to generalize. I had a 1st generation 18-70mm DX Nikkor zoom. It was just a poor lens. Poor fit, focus uneven across the frame, and just generally not good. Don't even think of sharp, even with the 6 and 10 MP cameras I was using it on.. But a later version of that lens, which I got along wiith a D90 IR conversion, is quite nice. No comparison to the first one. It's still neither premium nor even a mid-tier lens, but it performs much better. And sometimes, kit lenses aren't cheap. The 16-80 f/2.8-4 DX Nikkor zoom is alomost $1100. Some folks really like it, but in my experience, it's no better than mediocre, especially for that much money, And it's also f/4 over almost its entire zoom range. Its full frame equivalent, the 24-120 f/4 Nikkor is a much better lens for about the same proce and is available used for much less money.

Mine was definitely a Nikon packaged kit lens ... NOT a vendors bundle. The kit came in a Nikon "master" box that listed the contents, including that lens and a reeeeally nice large kit bag. The kit has its own SKU number as a package. The body was a D610. The kit was priced at only $25 (!) over the body-only price at that time.

Similar situation with my 24-120 which came with a D750, a grip, and a (much lesser) kit bag. Those two deals are the only reason that Ive got a coupla Nikon SLRs in the closet. I use those lenses on Sony and Z bodies.

Depends upon the camera whether you should format or delete. Sony cameras should should be formated or deleted in camera. Sony maintains some sort of file structure that erasing somewhere else doesn't deal with, and holes are left in this file structure. For instance, you can't copy a picture onto a memory card on a PC, and plug that card into a Sony camera, and then see that picture on the camera.

I also have Olympus cameras, and they do not have the Sony behavior.

Don't know what camera the OP was using.

One thought would be to quit formating after every use. Its not good for the card. If you wanna clear out stuff, just delete it.

Its great that your camera can see pix on a card thaz been through the rescue procedure. Cameras are usually unhappy with files that have been "meddled with". Most typically even if the camera doesnt see recued files the PC will see them.

The rescue that I have done, just once, renamed all the files. That was enough to confuse the camera but not the PC. But in your case it seems the opposite has prevailed, and good for you !
No just the ones from the games I had lost. You mentioned I should quit formatting the card after every use and deleted the images. I have always formatted and never had a problem.
A few files on camera card failed to view in-camera cuz I had rotated them in a PC viewer. Even after rotating them back via the PC, the camera still could not display them due to that meddling. Rotating back doesnt remove the rotation tag. It just adds a 2nd tag in the opposite direction.

BTW, its clear that youve got your 800 hockey pix back now. When you saw those in the camera, were the 5700 "rescued" earlier pix now showing up again, in the camera as well ?

No expertise in recovery apps, but heres a possibly useful idea.

Offload that 5700 to some temporary storage by copy-AND-delete. Then if the 800 are still hiding on the card maybe a second running of the recovery app will find them since they are now supposedly "the only stuff left".

I put that in quotes cuz, as youve now discovered, even after a format, stuff is not ever really gone from a card. But my hopeful idea is that the 800 will now be "less deeply buried" and the app might find the 800 instead of the 5700.
Worth a try.
Thanks
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Since formatting is always risky, maybe youve also proved for yourself that theres no real space to be gained from doing it as constantly as you have been, and yet theres always the risk of a misstep.

Best of luck to you with all this.