I am still not sure why so many twitterers and news reporters report the absolute daily figure for positive results without mentioning the issue of whether tests have increased
I'm not sure whether that is really as much of an issue as you think. It's more the positivity amount that would be relevant.
If there are more people with symptoms, especially if they've been in contact with a positive case, then you will expect more tests to be needed to be done.
So you would expect tests to increase when more people are positive.
Also the general public seems to be pretty statistics illiterate, so if you start confusing things by saying "X positives and Y tests" they'll not be able to tell the difference between:
Yesterday: 100k tests and 10k (10%) positivity
200k tests and 20k (10%) positivity
200k tests and 30k (15%) positivity
200k tests and 10k (5%) positivity
Looks fairly easy to work out if you're reasonable at maths. But the numbers are more likely to be 426 382 tests and 52 438 positives. Now as a mathematician I would fairly quickly go to 425k/50k: tests/positives approximation, but the general public wouldn't.
But it also isn't that simple. You see the number of cases today isn't from today's tests. Or even simply from yesterday. You have about 5 days worth of tests. One might be a low data day, one might be the highest ever... so you can't split it that easily.
Looking at the number of cases from specimen date would work, but then you're looking at a lag of 5 days, which when things are moving so quickly can feel too far away.