Use Cases

How about business hours 1st field open time and 2nd field close time?

How about phone number if 1st field and extension in 2nd field?

I have found the need for key/value pairs exceedingly common - I've used a version of this module on almost every work project I've had to so far.

X-Y pairs are the most common example, but also Merchant ID / Terminal ID for credit-card readers. They're almost never directly user-facing in my experience (handled via a custom widget), and highly dependent on project, but also very common.

Yes you can. Just add the double field twice and rewrite the output for each token value. In my example, these are the token values for example field:
[field_user_shop_hours] == User: Business Hours
[field_user_shop_hours-first] == Raw first
[field_user_shop_hours-second] == Raw second

So, you could create the first double field with rewrite output to the first subfield and then the second double field to the second subfield.

Just a note that using raw values is potentially dangerous. Use Strip HTML tags checkbox in Rewrite results section of the view to prevent XSS vulnerability.