This should be called "Multiclassing" or "Cross-Skilling".
Subclassing implies a deeper, sub-level of an existing class. Giving you access to other class skills is not going deeper, it is broadening your options. There may be a "deeper" level of customizability, but this is not a sub-class.
I would like to see the concept renamed so it fits with the big RPG, Dungeons & Dragons. Sub-classing (or prestige classes) are separate to multi-class or hybrid classes.
What I would also like, in a further exploration of "sub-classing" as if is named, are:
1) incentives to try different combinations. For example, unique cross-class skills or combinations. Minor, but flavourful elements. They can be recycled for any such combination. E.g., taking Necro/Warden/Sorc pets in combination gives you a small buff that lets you run +1 pet or gives your pets 5% HP. If you take a Frost/Lightning/Fire skill tree, you get a slight buff when you cycle between each damage type. This is what I would. Consider "sub-classing to really be, a reward for specializing your class by taking elements from other classes to build a new, distinct identity (but related to the main class). Perhaps there could also be "oppositional" rewards. I can't imagine a Templar is permitted to easily become a necromancer and/or an Arcanist, maybe they lose some resistances or have a healing debuff, but gain a minor flavorful reward for learning about their enemies powers.
2) Some "core" class skills or passives that exist outside of the class skills lines. For example, Sorcs may get a unique lightning buff, DKs fire, NB poison (but hopefully more interesting than just damage). This keeps classes slightly more distinct. This could also be a purity buff, E.g., a reward for staying a full Warden, instead of ditching one Skill tree for a different DMG one. Perhaps a skill cost reduction, or multi-using that classes skills gives a reduction in a resource cost. Maybe a unique benefit for having one of each of your classes skills trees slotted.