I hoped this was going to generate some more discussion, but that's not really happening, so I'll just elaborate on some of my thoughts.
To me, strength of a dragon comes from the number of scenarios in which is it above average usefulness compared to the number of scenarios in which it would be average and below average. That largely ties in to when it is hitting for weakness, versus just hitting normally, versus being hit for weakness. Additionally, I mostly care about strength in terms of the Masters arenas. Before that, the same strengths will apply, but the meta may change enough that things are drastically different in terms of what dragons are common.
Let's assign a 1-5 rating scale to the dragons for each of their elements, based on their usefulness in that element's arenas. I propose the following scale:
This is the minimum value, earned for having access to arenas 1 and 2. Dragons get a 1 for an element if they are weak to attacks of that element and they have no counter attack options (i.e. no ways to hit attackers of that type for weakness). For example, a dragon whose main type is Sea might receive a value of 1 for the Nature element, if there are no other mitigating factors.
This represents a dragon whose main element is not weak to the element in question, but is weak to a element found in one of the common meta dragons for that element. The clearest example here is a dragon whose main element is Flame who also has the Pure element. With no other mitigating factors, that dragon would receive a 2 because of Kratus.
This represents a dragon who has no specific weakness concerns, or who has counter attacks to cover those weaknesses. This is the average case scenario, in which the dragon also has no specific strengths to make it better than average.
Dragon qualifies for 3, plus either hits for a relevant weakness in arena 1 OR can be used in arenas 1 & 2. This is sort of subjective, since technically most dragons with a 3 rating should fit one of those two factors. Think of this as sort of a 3+ rating for dragons that are subjectively stronger than average but not so strong as to qualify as a 5.
Dragon can be used in arenas 1 & 2 AND hits common dragons in one or both arenas for weakness. An example here would be a dragon with Sea as its primary type, and Pure as another of its types, enabling it to decimate Kratus dragons.
Note that these ratings can vary over time, since new dragons often become meta-relevant for a while. It is expected that Kratus will always be relevant. All breedable legendaries are likely to be considered meta-relevant for their elements. Dragons who have a history of performing at the top of a given element are also considered meta-relevant (such as Horai, Root, and Forest Queen for the element of Nature).
An additional consideration is elements that are inherently weaker or stronger. Some of these could be factors in deciding between 3 & 4 for a given element. Metal is a less common element for most meta dragons. That makes Ice and Terra elements a bit stronger than average (though War quickly takes away this bonus for Terra). Further, since Light and Terra hit exactly the same weaknesses, a dragon which has both is going to lose a couple of points of value. Dragons with Light as an element very often come with Dark as well, so having Light as your main element loses you a point or two as well (but there are enough common Dark dragons without Light as an accompaniment to keep Dark from suffering this disadvantage, at least to the same degree).
I welcome any thoughts and opinions about this fledgling system. I'll reply again with how I would apply it to rate the dragons listed in my original post.