No,I'm talking about the fact that John took over was the triumph of proximity of blood over primogeniture.
Not as bluntly : you didn't have established succession laws, that appear more from custom and precedent than a CK II-esque decision "well, we're gonna switch to primogeniture now".
Basically, John's rights had such precedent for what mattered to England or some lands as Normandy; while Arthur's rights were more based on French customs (Angevine, Breton, etc.). And eventually John's capacity to rule as a king being more obvious than Arthur's, it made him won the day rather than an anachronical legal conflict.
Of course, their respective supporters were more from the relevant regions : pointing again the disunity of the so-called Angevin Empire. It doesn't mean you had a clear clash before : Henry the Young was crowned during his father's reign (as it was customary up to this era in France as well) for exemple, in order to reinforce his succession.
Eventually, John still had to deal with Arthur and having him dead, because primogeniture had enough base to live on (and did so after him).
Again, except deep succession crisis, the primogeniture succession had enough precedents : John's accesstion wasn't the triumph of anything (it didn't lasted as a precedent, quite at the contrary) and was more about the formation of precedent and succession customs than a clear fight between them.
Now, you're not wrong strictly speaking, but I just want to point that one shouldn't systematicalise and rationalise concepts that weren't yet formed as such.
In all case, it's a bit irrelevant for the case at hands, as in Plantagets conflicts during Henry II's reign.