How do you deal with IT costs that aren’t under the IT team’s direct control? For example, cloud usage costs driven by other departments.

We measure them im dollars versus the value, or perceived value, the deliver.  When these other departments want to spend more money on technology/technology services, we always review what current spend should be eliminated to fund their new spending.

We used to do Charge-back, which was fairly effective.  Now we do Show-back, which is less so.

I would prefer to use policy to align cloud spend with an actual budget, and thus warn, then turn resources off, but that has been deemed to be an unacceptable risk to revenue generation."

My experience: We moved from showback to chargeback. it was a little complex process as we needed to involve the BUs and Financial Teams. Generally speaking now there is more commitment and collaboration in managing optimization for costs. Obviouslu a key activity was to develop a dashboard for exec and technical teams where the costs (and the forecast) are visible in near real time.

Costs that are under direct control of the (internal) consumer make for much easier conversation that overhead costs from IT.  As long as sufficient transparency exists, they are the part of IT costs where the consumer can feel in control of their IT costs, as opposed to other costs that often get arbitrarily allocated.
If there is not a chargeback mechanism, to these other departments, then nobody is going to feel accountable for these costs and if they then become allocations to a business unit, this can create a difficult situation.

The general principle here is to move costs to where a team/person recognizes the value and is able to take a decision on optimizing Value/Cost equation. 

Chargeback is more effective but involves administrative overhead. Showback is less effort intensive.

This as an administrative overhead. So, it is important to build awareness that this is all about IT Cost Optimization for the enterprise. 

You can also look at mapping your cost elements on a 2 x 2 matrix and build an approach for each of the 4 categories.   
- Directly Attributable Costs vs Not-Directly Attributable    
- Fixed Costs vs Variable Costs

1) Fixed + Not Directly Attributable (Data Center Costs)..   Don't Chargeback/showback
2) Fixed + Directly Attributable (Cost of N/W Connection to a Factory Site)..    Chargeback/showback
3) Variable + Not Directly Attributable (Citrix Farms. RPA Automation)...   Package as a unit service. Allocate costs for chargeback/showback.
4) Variable + Directly Attributable (Cloud Resources for an application) ... Chareback/showback