I'm bringing back this old topic, because I'm thinking about writing/drawing/maybe even programming something, and I don't want to get the magic all screwed up. The problem is that it's also been a long time since I last played Chrono Trigger.
I've skimmed through this thread, reading good parts of many of the posts, and I think a lot of the ideas here are too focused on the elements that exist or the idea of a single real source of magic.
I'm pretty sure that all of the types of magic used in all Chrono games come from a process that involves the concentration of energy or life force (e.g. the cycle of life and death such as with a planet's life stream, large and highly evolved organisms such as lavos, or solar energy such as with the sun stone). As organisms live around these energies, they evolve to tap into them and use them. That's why Ayla can't use magic, but Crono can.
In this aspect, Mystics are more capable of using magic, because they're higher up on the evolutionary scale in terms of magic. Humans moved away from being able to use magic for the same reason they don't have tails anymore: they don't need it.
There may also be other reasons related to events happening after the fall of Zeal, possibly involving a backlash against strong magic users by the majority of people, who couldn't use magic anymore.
Zeal was originally built out of the power of the sun stone. The nobility and royalty of Zeal became so, because they were the first magic using humans. They probably lived in clans near the sun stone, and as their clans advanced, they built cities and soon learned to make machines that could take advantage of the sun stone's energy.
Of course, many non-magic using citizens existed in this society, since the Earthbound ones were said to come from Zeal. Machines and cities, not to mention large numbers of people, create a heavy draw of energy (look at our electricity usage today compared to fifty or sixty years ago). Eventually a source such as the sun stone would wear out, which is why the discovery of Lavos was so important to them.
The first evolutionary step in magic use is being able to use energy from a strong, concentrated source (e.g. Sun stone or lavos) to create magic effects, although it may require they stand in a refined source of radiated energy for a period of time (e.g. the Mammon machine). This is how many Zealians used magic, and why they couldn't after the fall of zeal.
This first step starts with being able to use magic through direct contact, then being able to temporarily store magic energies for later use.
Elements from CC can be considered a store of energy created and refined to a specific element over time from small sources. Users are still creating the magic effect, even though the energy used comes from the store. Because elements are highly refined into specific forms (e.g. a Heal element has healing properties), they are easy to use for any creature evolved in channeling energies. They're like magic batteries.
The next step is evolving to be able to refine your own energies to use magic with. This is how the Zeal royal family used magic, although using other sources such as the Mammon machine magnifies their power. This ability can become innate however, if a species doesn't make use of it.
This step is similar to creating elements within your body. Kind of an element glucose. Different people would naturally evolve to be able to create different types of element glucose, although highly evolved beings (e.g. Magus) could create many sorts of elemental glucose.
Magic using humans became more prevalent in Zeal because they used magic, and also due to their close-proximity to refined energies (just like living on Earth causes creatures to evolve eyes because there is light). After Zeal, there was much less exposure to these things, so humans naturally moved away from magic (many deep-sea creatures are blind).
However, so long as technology does not fully replace magic, humans would still evolve towards being able to create energies. After all, some creatures in the deep sea evolve to see, although there's no naturally occurring light down there. They evolve to create their own light.
So then, why can't Crono use magic to begin with? And how is Spekkio able to make him use magic? The answer is simple, Crono is already advanced enough to use magic (that is, create his own magic energy). However, having never used it his body doesn't bother refining any.
What Spekkio does is create an initial store of refined element glucose in Crono that allows him to use basic Lightning spells. Being exposed to this, his body learns to create this special glucose (which it already did in a less refined form, allowing the Slash ability). By exercising this new skill, Crono's body is able to create more refined element glucose that can create even greater lightning effects.
When Magus transforms Glen into Frog, he changes many parts of Glen's genetic makeup. Frogs, living in water, have greater tendencies towards evolving magic abilities related to water. After all, they spend most of their time in it. This means Glen as Frog would be more inclined towards water-based magic.
Also, the idea the Lavos would try to speed the evolution of magic refining life forms makes a lot of sense, since Lavos is a high-energy life form, and requires very refined/concentrated sources of energy to survive and reproduce. Causing these beings to then advance towards technology use would ensure that they would spread in great number.