Is it by any chance the case that, historically, the い-adjective ending 〜かった is a contraction originating from 〜くあった, where あった is the past inflection of ある?
That's exactly what you're seeing.
For ～い adjectives, there were three base conjugation forms:
- ～し -- 終止形【しゅうしけい】: terminal / conclusive, for ending a sentence of clause.
- ～き -- 連体形【れんたいけい】: attributive, for modifying a noun or other 体言【たいげん】 (uninflecting word).
⇒ The ～し and ～き forms are fused in the modern language to just ～い.
- ～く -- 連用形【れんようけい】: adverbial, for modifying a verb or other 用言【ようげん】 (inflecting word).
Classical grammars often also include:
- ～けれ -- 已然形【いぜんけい】: often treated as the realis for things that are definite, or are becoming so, or can become so; superseded in functional terms by hypothetical or conditional usage, resulting in the modern term 仮定形【かていけい】 or "hypothetical / suppositional / subjunctive form".
That said, some authors postulate that the ～けれ ending is also a fusion of ～く + something else, often suggested as あれ. Personally, I don't see how //ku// + //are// could possibly become //kere// just on phonetic grounds, so I wonder if it must have been something else.
You can see a bit more about this in the conjugation table at https://ja.wikipedia.org/wiki/形容詞#ク活用. The so-called -kari conjugation pattern clearly shows the ～く + ある fusion.