The question here is if moving images from one medium (such as a negative) to another (such as a digital file viewable on a monitor) can be done without the image information being altered.
That's an easy one to answer. Obviously, it can't!
In my opinion, optical printing exists a similar media move issue. There is always differences between before and after the move transaction of the image data.
So apart from the other things you said, which I understand, but only partly agree with, the question is: what do you take away from this?
You started with the question how to judge your C41 development process. For many reasons, relying on the output of a scanner isn't a very good way to do this unless it's part of a carefully calibrated imaging chain, which is likely beyond the means or necessity of a home user. An approach relying on optical printing is similarly challenging.
The question remains how relevant it is to know the quality of your C41 development process beyond the obvious informal assessment of just producing images and seeing if they meet your needs. I understand your imaging chain is purely a hybrid one, where you use film for capture and then scanning to proceed into digital post production. This means that there are roughly speaking four areas where the quality of the output is determined (or, if you're cynical: can be messed up):
1: Choice of materials; film & chemistry, but also equipment like scanner and development tanks etc.
2: Film processing
3: Scanning
4: Digital post processing
To an extent, all of these items are black boxes. But some have more potential for both mess-ups and quality gains than others. Let's see:
#1 is a simple one: we have very little influence on the materials, so the best shot we have is to buy materials from a reputable manufacturer and use them before they go bad.
#2 is for the home user likewise a black box for all intents and purposes, because even if you determine that the process is out of spec, it's often difficult to figure out why. On the other hand, a process that's run on decent materials (see #1) and according to the manufacturer's instructions combined with common sense tends to perform more than adequately for virtually every purpose.
#3 you can either work in a color-managed workflow using calibration targets, but the problem is that this only goes so far and relies on targets on the exact type of film you're using (and a scanner that actually supports such a workflow). The alternative is to experiment with various scanning settings to find something that seems as consistent as possible, and then hope for the best. Outsourcing scanning is a third option, but this makes the black box only blacker still.
#4 this is a part where the artist/photographer has a massive degree of control and opportunities to steer the result into virtually any imagined direction. The limitations are posed virtually only by the user's abilities/competence, given that he starts with something that's halfway decent (i.e. evenly developed film with at least somewhat useful color data).
Given the fact that your odds of actually making a difference in terms of the end result are very limited in #1 through #3, with basically your best shot being "just do as it says on the tin", it seems very obvious to me what the question should really be about.
So my honest answer to the initial question you asked, is: go read some books on color grading. As long as you can produce negatives that don't have horribly apparent defects, this is the one area in your workflow where an investment in time and perhaps some software is really going to pay off dramatically.
You perhaps now also understand why the vast number of photographers have transitioned to digital. It reduces 3 pcs. of black boxes to just one, leaving their hands free to focus on the fourth, which actually really makes a difference. This is not me being cynical about the possibilities of analog photography etc. It's just a sober observation of how people who are serious about the craft and approach matters rationally produce images.
An irrational approach I find very interesting and in fact I would encourage if you're inclined to it. But if you choose that route, don't tire yourself with boring questions about how to get your C41 process running on spec.
Oxidation prevention by HAS is static. Agitation is dynamic.
It's unclear what you mean by 'static' and 'dynamic' in this context. The chemical processes that occur in an agitated developer are very dynamic indeed; there's nothing static about them. This is true for all processes within the developer given the innate mobility of molecules at higher than absolute zero temperatures. HAS is not the chemical equivalent of a piece of saran wrap being pulled over a pudding or something. Its protection is as 'dynamic' as can be. You seem to doubt that the amount of HAS present in a commercial C41 developer is sufficient to protect a small volume in a rotary tank from getting into trouble in one (or even a couple) of development runs. This is not the case.
Also, in my experience, C41 developer that's used (with constant agitation) preserves just fine and will work virtually the same weeks after its first use. It's something I don't recommend because repeated use will eventually result in drift, but the developer doesn't magically oxidize all of a sudden after it's been used once. This is evidenced by the lack of color change - don't be confused with sensitization and antihalation dyes from the film leaching into the developer.
Really, you're making far too much of this supposed oxidization problem. If you use your developer one shot, or even twice, it's not an issue. Not even if you go crazy shaking it during processing (it evades me why you would, however). Storage conditions are far more relevant.
TL;DR: it's very easy to get lost in details that turn out to be irrelevant, and to complicate matters that are unproductive. In my view, you're heading down this path very fast. That's OK, but if you want to make images, this is not really the way to go.