I don't agree that Terapagos has time travel.
Unless GF’s writers are playing 18-dimensional KerPlunk, the verbiage that’s exchanged in the Crystal Pool scene is pretty blatantly discussing time travel:
“Have I somehow broken through the boundaries of space-time?”
“From the clues you’ve let slip, I suppose I would have to conclude… From my perspective, this must be the future…?”
“I do…have a family. A son. He is probably at home right now… Well, no, I suppose ‘right now’ could be inaccurate. Whenever and wherever he is, I imagine he must be…quite lonely.”
Plus just the general fact that the Professor, during that scene, has explicitly been struggling to make a breakthrough in their research, which is resolved by you giving them the White Book, which their journal notes in the Underdepths mention you doing.
Then there’s the emotional throughline with Koraidon / Miraidon, who are clearly happy to see the Professor again, and sad when they depart. It was said that the Crystal Pool allows you to see people who have passed on, and that turns out to be sort of true, in a time travel-based way: Koraidon / Miraidon is afforded one last moment when the Professor who died protecting them.
I don't really agree that the Paradox Pokemon have time travel elements, in general.
Then it strikes me as an odd choice to call them Paradox Pokémon, and to correlate them with the distant past / future and a device called a time machine. Those trappings are what they’re always going to be associated with by the audience.
I think it's more likely that the Expedition team had ideas of grand creatures that Terapagos turned into a reality, which were then recorded. IMO this is supported by the fact that one of the Pokemon brought was Heath's Cyclizar, which would possibly add the idea of altered versions of them.
See, the thing is, I sort of get this, because I believed in the Imagination Theory for a long time. But I did so more because that theory originated from Khu, who at the time, had leaker cred. When he ended up getting a bunch of predictions about the Indigo Disk wrong, and the only further development on the origin of Paradox Pokémon provided in ID was that they come from alternate timelines, I discarded all of my pre-colored assumptions and sort of reanalyzed the story, taking into account only what it actually says about everything.
And the conclusion I arrived at was, well, sort of what I said up above — that I have a very hard time believing GF would bandy around ideas like a time machine, past and future Pokémon, other timelines, scenes with all the trappings of a bootstrap paradox, the very word “paradox,” dragon mascots whose names contain the words for “past” and “future,” and version-exclusive professors wearing cavewoman garb and a Tron suit, only to secretly intend for players to decipher that there’s really no time travel going on at all, and that it’s
actually all just wish-granting, which not one single character in the story ever even
considers could be the case.
The other thing is - I would argue, anyway - that the Imagination Theory is even more vague in some ways. Like, okay, Terapagos manifested the visions of strange Pokémon in the minds of Heath’s team. But why were they picturing these sorts of Pokémon? Why, in one game, do they imagine primordial-looking creatures, while in the other, they think of futuristic ones? Why is the sketch of the Beast / Sword hybrid not manifested directly, but rather as three separate creatures?
If it’s a bootstrap paradox, then the difference is accounted for by the involvement of a different professor. Sada, personally, is fascinated by primordial aesthetics and ideas, and Turo by futuristic aesthetics and ideas. Whichever professor is the prominent one in the game is determined by the contents of the book that was published, which is determined by the creatures that Heath’s team saw, which is determined by the creatures brought over by the time machine, which is determined by the professor who built the time machine. It’s a self-perpetuating loop.
In my opinion the idea of ancient and future Pokemon in general just doesn't really make sense, even for Pokemon, in this way at least. Especially the Future Pokemon. Despite them being based on a cool concept (the idea of Pokemon going extinct, thus people make fake versions of them) it also kinda makes no sense.
Nowhere was it said that the future Paradox Pokémon are “fake” versions built by people. We don’t know why they are the way that they are — the only details given about them are from a silly tabloid; the Pokémon equivalent of Weekly World News.
If they’re just from some alternate timeline, which is the closest we get to an actual stated backstory for them, then it doesn’t really matter, because that timeline could and probably does have a totally different history from the main timeline.
For instance, Paradox Suicune, Entei and Raikou don't make sense for obvious reasons - The normal versions of them have only existed for a few hundred years.
While you could argue that maybe Ho-Oh just made new Pokemon within the species or something, these are the first sightings of them. It can possibly be explained but I still believe that they aren't actually real Pokemon that existed in the past.
I don’t believe that Wake, Fire, and Bolt existed in the past of the main timeline either… but again, an alternate timeline from which they were imported wouldn’t be constrained by the same history.
Them being from an alternate timeline, and only inhabiting a future
after the Professor’s time machine is built (a future which is merely being glimpsed by the research team via Terapagos), would also explain how the sketch artist could draw a mashup of Raikou, Entei, and Suicune 50 years before they were created by Ho-Oh — the artist actually saw Wake, Fire, and Bolt, and combined their traits into a sketch of a purely theoretical creature.
Terastilization as a mechanic does not really have anything in common with it either.
I don’t think the effects of Terapagos’s influence all need to be linked to one underlying concept. Its existence causes all kinds of things to happen. Time travel, Terastallization, the growth of Herba Mystica, the amplification of machine capabilities, the formation of Tera Raid dens, some sort of effect on Glimmet and Glimmora… I think Terastal energy is just a very flexible energy source that can do a lot of things.