> IMHO, every org along those lines would benefit from an independent IT tiger-team whose sole job it is to find business problems and apply technology to solve them
You're describing external consultantcies. Some are good and do as you describe, but some are bad and work simply to find more work.
Not in practice, unless they're signed to a guaranteed, multi-year, cross-org contract. Fixed price has so many issues. Hourly has its own Pandora's box.
The incentives (mostly turn time) are just too misaligned to create good solutions, even with good consultants.
Consultants also aren't empowered to fundamentally push back on a client's demands, nor have existing relationship with other IT orgs they'll need buy-in from to get durable work finished.
You're describing external consultantcies. Some are good and do as you describe, but some are bad and work simply to find more work.