Another idea of testing is to see how much a driver can nail it, or push it.
Lets say this, with the constants being known downforce and a known track with constant conditions, and the driver not being given any data appart from tyre brand:
Run 1 = Known brand rubber A - 1:25.6
Run 2 = Known brand rubber B - 1:24.9
Run 3 = New brand rubber A - 1:25.4
Run 4 = New brand rubber B - 1:24.7
Run 5 = New brand rubber C - 1:25.1
Only one of the brands was a new brand at a test, and it wasnt B or C. It was actuallt brand A that was the new rubber, and it was theoretically faster than known B. Now thet change the brands about a little and tell the driver that New A is Known A and he goes a full second quicker than the previous run. Thats what testing is for, its for testing a variable against a known or a known set of results.
Its only when you have a driver that goes out on a Known when you have put on a New and he goes slower that you worry a little, however you keep chaging the running order and when you come to the same result again and again you worry and then go back to the drawing board, or race the new item if thats what the results are showing.
Sometimes going to the back of the car and ratteling the spanners about under the bodywork can often lead to a increase in pace in a driver, Thats the unknown that you have to get to become a knon. And thats why testing is so desireable, getting the driver conditioned to the point the driver just performs like a known. The best known drivers in F1 are the ones that have tested cars to the moon and back, at least a couple of times, De la Rosa and Badoer are the ones that spring to mind, bud Wurz and Gene arnt far behind also.
Once a unknown is known, they can then start to change other areas and bolt on performance in other areas quicker and easier once every part is fully exploited.
Sometimes you have to go back a few steps to re-baseline against what worked best last to get a true refection in car improvement. Hence why you can see a car top one day and last the next, they have "reverted to settings that worked last" just to see a reflection in performance. Its also why teams want to have at least 3, but ideally 4 or 5 drivers sometimes in the car to A/B results using a pre determined run plan that they will all do.
All of this is cost, and why testing has been restricted in the past 3 years to just 18 to 19 days a year for the last two years.
Personally, i think testing is required, and would have helped all teams in the past 2 years, the 3 newbies from the 2010 entry would have been able to dial in much quicker and been much closer by now. But i have always thought that testing should be allowed, but in a manner that is justafyable performance wise to cost base.
If it were me id have each team have a maximum of 12 pre season test days, 10 in season test days and 6 post season test days. Limit race drivers to just 5 pre season days, 4 in season days and 2 post season days is a way to manage the driver duties to make sure Test Drivers and Young Drivers get a look in, and also a way for teams to finance those days thrugh young guys. Id also instruct Pirelli that they can only give teams tyres at those tests and thus stopping teams testing on their own outside the RRA, if a team wants a set of tyres from Pirelli for events outside theese paramiters, the rubber will be outside the remit of F1 grade, either being too hard or too soft for any results to be conclusive.
Testing is a necassary evil, it gets results, and sometimes you test without something new just to test something else out, say a Data Engineer will engineer the whole car that day, also a No.1 mechanic may be tasked with running the team for instance that day. It can be for the eventualities that sometimes arnt always shown that you test.
Sometimes its about the car, sometimes its about the team arround the car thats tested. Its about getting those unknowns to become known.