3/3
To reiterate, the anime PROBABLY went with the Energy-Theory (it's my guess, I'm unaware of any interviews opposing that). Or, it was always about the Shrink-Theory, but with all these misleading hints, it was just natural for non-Japanese people to believe the Energy-Theory. And pre-PLA, most hints were so trivial that they would support either theory, or well hidden. Granted, most plot points are just one-offs, yet they still add to the overall worldbuilding.

Concluding, it is retarded to argue the games support the Energy-Theory, as they were either neutral in this regard or left clues in favor of the Shrink-Theory. But it's also disingenuous to call the Energy-Theory a headcanon, since the anime as official media hinted at it on multiple occasions. In other words, Shrink-Theory is the original concept idea behind capturing pokemon, Energy-Theory is (or was, before PLA "re-retconned" it) the anime's spin on it.

TL;DR: The anime is probably the reason why the Energy-Theory exists.