Oh, yea, go with the Belial account. Between the impact Belial offers over literally every other fire eidolon and the rarity (you will most likely never roll a 100% eidolon through jewels), from a pure practicality perspective, I'd say you probably would need to roll 4 foundational pieces to even start thinking of turning down Belial. Possibly lower it to 3, if 2 of them are of the same element. Other people will of course have different thresholds.
By foundational piece, I mean a kamihime that has a good argument/minimal strings attached for being placed in a high end team for that element. A gacha eidolon that is not a 100% eidolon automatically counts as a zero here. Fractional is possible; I count Michael and Tyr as 0.5 each, for example. Gaia, Svalog, and light Tsukuyomi are easy 1's. Shiva and Acala are 0's.