I am asking if the developer is to be used as one-shot or can be reused with extending time.
Because Kodak has not published any time correction past 4 films, unlike other manufacturers.
Kodak is basically being conservative with respect to "quality" standards. More specifically with respect to the "process control charts." This is where someone periodically processes a pre-exposed "control strip," measures the resulting test patches (using a status M densitometer), and compares them against the manufacturer-supplied "reference strip." There are also standard spec limits (tolerances) for the differences. (See Kodak's Z-131 (I think) for more information than you probably want.)
If you stay with the Kodak guidelines, and you have more or less average exposures on your film, you will most likely stay comfortably within the process spec limits. If you go beyond Kodak's guidelines, say double, you will most likely get some of the color plots dancing outside of the spec limits. Is this a problem? Well, it depends. It certainly would NOT be professional-level processing. But if one always (only) scans film...?
FWIW "time corrections" are not a normal thing within the official C-41 process.
Regarding different brands of C-41 developer, these are all fundamentally the same. (If they were not they wouldn't be able to match the process "activity" specs.) So when you see claims for extended roll counts being processed per unit of developer, most likely the chem maker is simply working with more, uhh, relaxed tolerances.
FWIW this is one of the things I worked with for years and years, in an outfit where we ran something like 40 to 50 control strips EVERY DAY. (I probably taught a couple dozen techs, over the years, how to troubleshoot process problems, etc.) We had done hundreds and hundreds of chemical analyses, mostly partial, on color developer solutions when studying effects on control charts, etc. There really is not a lot of mystery to it once you see some analytical data vs control chart plots.