This is something I was aware of when I used Kodak chemicals but since I use a Jobo and continually agitate the film I have never tried it. Secondly I am presently using inexpensive C-41 kits from Freestyle so I'm not really sure how replenishment would work with those.
Hi, I'd say that the Jobo rotary system automatically rules out replenishment of a color developer. (Unless, perhaps, if you found a way to fill the tank with an inert gas, etc.) But just for general background information see below:
Regarding the "inexpensive C-41 kits" I don't know the makeup. But if they are specified as "developer replenisher" AND spec a low replenishment rate (similar to Kodak's LORR) then they should be roughly equivalent.
Fwiw the spec replenishment rate tells one a lot about the replenisher. One of the first things a "proper" replenisher should do is to dilute the development byproducts back down to the original spec concentration. Kodak's LORR replenisher specs a rate somewhere around 26 ml/roll for certain lower speed films (Portra 160 for example). Since we (or at least I) mostly trust Kodak's tech information) we can conclude that this volume is enough to dilute the byproducts (mostly bromide ion) back down to spec.
There are other replenishers that are designed for significantly higher replenishment rates. On the surface it might seem that these replenishers would over-dilute the byproducts, but not so (at least for a proper replenisher). What they do is to already contain the equivalent of SOME byproducts such that the replenished "tank solution" stays at the correct concentration.
The next thing a replenisher should do is to bring the concentration of the developing agent back up to aim concentration. So one can probably see that a low-replenishment-rate system needs to have a higher concentration of developing agent, compared to systems using higher replenishment rates.
So these two things - developing agent concentration and "byproduct" concentration in a replenisher need to be different according to the aim replenishment rate. Meaning that the design replenishment rate for the specific product pretty much determines the makeup with respect to these two things.
Now, if someone is concerned about getting the maximum economy out of a replenished system (and assuming that such a system is feasible for them) here's one way to look at it. When film leaves the developing tank it is wet, meaning that carries out some of the developer; this amount is "lost." On top of this any excess volume due to the added replenisher is also lost (has to be discarded). So obviously a higher replenishment rate system produces more waste material. And obviously throwing away more excess developer volume than necessary is not the most economical use of the chemicals.
Anyway these are just some general things about C-41 developer replenishers that are not immediately obvious.
Fwiw the "secondary" chemicals are generally also replenished in commercial operations. But for a small scale user the situation is different. Carry over from the previous solution, including what carried in the tank and reels, can dilute things excessively. So the chemical cost savings are nowhere near what a commercial processor, keeping carry-over at a minimum, can do.