It depends on who does your investigating, and the two cases are different in kind.
If you outsource investigation to your core, a case resolved before investigation is a case you never send, so your core never bills the per-transaction fee. At a modeled 35% rate, an institution with 100 disputes a month that outsources investigation avoids roughly $15,600 a year in core investigation fees.
If you investigate in house, the return is staff capacity rather than cash: about 15 minutes per intercepted case. At 100 disputes a month that is roughly 5.7 hours a month, or 0.03 FTE. Below about 250 disputes a month, this is capacity to absorb dispute growth without adding a person, rather than a saving you can bank.
The two are alternatives. An institution pays the fee or spends the hour, never both for the same case.