Understood. I wouldn't actually want it to recalculate on every API call, either. Control over whether or not a recalculation happens on a particular call (e.g. via an HTTP caching header or just a flag in the query params), or how often recalculations happen (e.g. every x minutes for spreadsheet y, every z requests, etc.), would be sufficient.
Even without control, just having better predictability around how often recalculations happen would be great. Right now, it's so unpredictable, I never know if I'm going to get a recent value or a value that is hours old. Knowing that recalculations are guaranteed to happen in any Sheets document in the worst case once every x minutes would at least allow me to select an appropriate polling interval.
As an example, right now I'm trying to take some information that a spreadsheet computes about my investments and surface it on my phone (and eventually wristwatch). For example, maybe I'll track my net worth or spending for a few months. If one wants a metric to move in a specific direction, one should start by being aware of the value of that metric, right? ;)
Eventually, I'd like to take other metrics (e.g. new customers today, bugs squashed this week, Amazon sales this month, etc.) and display them conveniently, too. Some of this information would already be in spreadsheets, and some of it is external and needs to be pushed/pulled from other systems.
Folks will argue that we should be writing scripts to do this, but there are good reasons to do it via spreadsheets. First, not everyone can write such a script, and many of those who can would probably end up making a spreadsheet anyway. Second, scripts like this require some degree of operationalization, whereas Sheets handles that for you (it's already Ops for running your business). Third, a single integration point like Sheets requires fewer integration connections than a point-to-point model. Fourth, spreadsheets make it easy to combine manually-entered data with live data. Last, the data from other systems are just that: data. People use spreadsheets to give those data meaning (or spin for corporate politics...).
So I believe that there's a lot of information that is trapped inside spreadsheets that people rarely see because they have to open up the sheets to see it; it's just too many clicks for someone who doesn't live in spreadsheets all day. With its API and the live nature of its documents, Sheets will let me surface that information so that more people see it, more often.
Well... enough proselytizing for today. I hope that gives you an idea of how I want to use the API,