They should but they won't - there's some structural finance reasons that banks like packages of the traditional ones for reasons completely unrelated to their performance characteristics and profit margins. Regulators are likely to be conservative in evaluating ISAs as an asset class, making them much less attractive for banks to hold as liquidity. Unless the same kind of political pressure gets applied as is working on behalf of the traditional class, I guess, but call that low odds I think.
Absent banks, you're left with large institutional investors (pension funds etc.) who want a higher ROI, which would drive up the costs and presumably slow the adoption of ISAs. In that scenario, you might have a few elite private institutions that have a large enough endowment to just hold the ISAs themselves until they're paying out, but they don't have much incentive to do so (their students can muster the cash up front easily) other than clout for being innovators. And they represent a tiny fraction of the total market.