I don't recall anyone mentioning a capacitor in the FS1/FS2 texts. Do point it out to me if I'm wrong. If I'm not, it's just another theory, one I don't give two ****s about because it comes from you, and not the writer.
And your point in this is... what, exactly? Similarly I could state that I don't give a rat's rear about you stating something impossible because it comes from you and not

... Whoever it was that decided to put fuel afterburners in TVWP can, of course, explain their reasoning in more accurate way than I or ngtmr-1 with our guesswork. But I do care, obviously, since I'm responding to it... Oh well.
Your original claim was that
There's absolutely no way you can introduce engines that run on time, replacing engines that run on fuel.
and since no one has introduced engines that run on time replacing engines that run on fuel, it's irrelevant anyway, but assuming you meant that replacing fuel-consuming afterburners with energy pool -operated boost system (which is what TVWP does)...
Yes, sure, it [the possible mechanisms on exactly how the afterburners work in canon FS/FS2] sounds likely. It is also unlikely that the engines are powered by the pilots urine. However, since we don't know how it operates (we weren't told), the pilot pissing and making it recharge, and there being some sort of a capacitor you learned about in your high school sci-fi class, are both equally acceptable theories, mostly because neither one matters.
Again, your original claim was that "there's absolutely no way you can introduce engines that run on time, replacing engines that run on fuel", and then you say that the proposed possible theories are not only possible but likely as well?
You conclude your post by saying that engines running on bodily fluids of the pilots is equally likely than plausible tech-based description, just because neither have been specified to be canonically true in FreeSpace universe... which is IMHO just some kind of strawman argument to distract from the fact that your original statement is equally wrong as any of the hypotheses proposed thus far.
True as it may be that none of these theories matter much because they can't be neither confirmed or falsified, that was not the point of this debacle. You simply stated that there was no way to plausibly explain why fuel-consuming afterburners of TVWP would have been replaced with energy pool -operated engine boost systems; you were wrong since there are multiple (more or less) plausible ways to explain it. With or without technobabble. Or urine.
The important thing to remember IMHO is that TVWP is not canon. I don't think no one is trying to claim it as such. Thus the transition from fuel-consuming afterburners to "time-consuming" ones is non-canon. And so are the ways to explain this transition. But claiming that there's no way to do it (in a plausible way, if I interpreted your post correctly) is not really anything but a sentence without much argumentation behind it. There are plausible ways to explain and there's no need to stick to canon, especially about things that are not mentioned in canon.
Besides, the best explanation is that TVWP makers want to introduce some variation to the gameplay, and making the afterburner limited by fuel rather than energy output capacity is one way to do that.
Is there some specific reason why you think it's unlikely that fuel-consuming afterburners were used before the switch to more familiar, FS1-era (and later) afterburners? In canon context, that is.