Hector said:
-It would make no sense for Goku to be that afraid when Freeza said, 'I haven't even used half my power,' if he had used only 10% of his power. If anything, he would have retorted with something like, 'Good. I haven't even used 20% of my power.'
Freeza hadn't been giving him the impression that he'd been holding back much, which was the main cause for his reaction rather than the amount of his peak that Goku was currently using. Moreover, Kaioken isn't something meant to be used in excess, so Goku wouldn't want to simply resort to it needlessly even if his greatest level was enough to trounce his expectations of Freeza's full power.
-How did Goku go from the tens of thousands to the millions in one zenkai when it took Vegeta multiple zenkais to reach that far?
Meta answer: Plot.
In-universe answer: Their personality is likely the deciding factor. Goku's more pure, calm and gentle spirit (ie. a major catalyst in what allowed him to become a Super Saiyan before Vegeta), would likely allow him to hone his Ki to a greater degree from the Zenkai when shouki and genki are two key factors in the total of one's Ki.
Why is it so hard for us to accept that Goku could do the same thing with the Kaioken?
Because Vegeta's bursts are something actively made apparent in the plot, as opposed to nothing supporting the invisible Kaioken.
The invisible Kaioken is such a nonsensical approach that it hardly even warrants being called a theory with so much against it, the most obvious counter being that manga is a visual medium and no visual cues exist even in the full colour manga of Goku using Kaioken until after Kaio notes he's using 10x against 50% Freeza, despite there being many visual cues beyond the red aura (Goku's hair spiking up as with SSJ during its uses on Namek, his eyes losing their dark pupils, the fact it's only supposedly "invisible" until those supporting it say it isn't, etc.). Combine this with the Daizenshuu making it apparent those involved have zero belief in it as well as Toriyama never alluding to its existence in future events, and the whole thing's little more than an excuse for people to not have the top tiers of the arc enter the hundreds of millions on the battle power scale.