Pamela Pecs Cytron, CEO of Pendo Systems, another provider of investment accounting software (See story below) said the call for modernized accounting systems has been a familiar refrain for several years.
Beware insurance companies that are licensed in lightly regulated jurisdictions, and make sure that those that you deal with have verifiable assets and verifiable audits from major accounting firms (and call the audit partner to verify that they actually were engaged to do the audit).
This happens mainly for accounting reasons: if the first call centre were to hand over all the information to the second one, it would bear the main cost of the call and make the second look more efficient.
The company should already be charging the most it can for that marginal phone call and a change in sunk costs might affect accounting profit but not that revenue maximising price charged.
There are no schemes to try to overcharge on overdraft by reordering the accounting process, but rather a live person will usually call you to say that your account has been overdrawn, and how we can help.