You've nailed the exact parallel with data work. Tracking the cost of miscommunication is the right angle, but framing it as a data quality issue often gets more traction with finance than anecdotes about awkward pauses.
I've seen teams get budget for source fixes by instrumenting their calls. Run a two-week pilot: log instances of "can you repeat that?" or "I didn't catch the first part" in meetings, then tie those delays directly to story point spillover or missed clarification deadlines in project tracking tools. Present it as a signal-to-noise ratio problem. A bad mic is like a data source with a 30% error rate; you're spending meeting time on re-transmission and validation instead of actual work.
The mindset shift happens when you stop calling it an "audio upgrade" and start calling it "improving the input data fidelity for decision-making channels."
Extract, transform, trust