Challenger was lost because NASA ignored a critical flight risk with the SRB joint O-rings. And by "ignored", I mean "documented that the risk existed, that it could result in loss of vehicle and loss of lives of the crew, and then waived the risk so the Shuttle could keep flying instead of being grounded until the issue was fixed". They didn't need more unmanned testing to find the issue; they needed to stop ignoring it. But that was politically unacceptable since it would have meant grounding the Shuttle until the issue was fixed.
Columbia was lost because NASA ignored the risks of tile damage due to their belief that it couldn't be fixed anyway once the Shuttle was in orbit. But that meant NASA also devoted no effort to eliminating the risk of tile damage by fixing the issue that caused it. Which again would have been politically unacceptable since it would have meant grounding the Shuttle until the issue was fixed.
Should such testing have been needed? No.
Was such testing needed, given NASA's political pressures and management? Maybe. Unmanned testing in similar conditions before putting humans on it might've resulted in a nice explosion without loss of life that would've been much harder to ignore than "the hypothesizing of those worrywart engineers," and might've provided the necessary ammunition to resist said political pressures.
The loss of the Challenger was the 25th manned orbital mission. So we can expect that it might have taken 25 unmanned missions to cause a similar loss of vehicle. But what would those 25 unmanned missions have been doing? There just wasn't 25 unmanned missions' worth of things to find out. That's also far more unmanned missions than were flown on any previous NASA space program before manned flights began.
Even leaving the above aside, if it would have been politically possible to even fly that many unmanned missions, it would have been politically possible to ground the Shuttle even after manned missions started based on the obvious signs of problems with the SRB joint O-rings. There were, IIRC, at least a dozen previous manned flights which showed issues. There were also good critiques of the design available at the time--which, in the kind of political environment you're imagining, would have been listened to. That design might not even have made it into the final Shuttle when it was flown.
In short, I don't see your alternative scenario as plausible, because the very things that would have been required to make it possible would also have made it unnecessary.
That doesn't follow. If those were unmanned test flights pushing the vehicle limits you can't just assume they would have gone as they actually did.
As far as the launch to orbit, which was the flight phase when Challenger was lost, every Shuttle flight pushed the vehicle to its limits. That was unavoidable. There was no way to do a launch that was any more stressful than the actual launches were.
Which mission are you referring to?
If it's STS-1, AFAIK there were no close call incidents during the actual flight, but the mission commander, John Young, did have to veto a suggestion to make that mission an RTLS abort instead of an actual orbital flight. Doing that would have been reckless, yes: Young's reason for not doing it was "Let's not practice Russian roulette."
One thing I wonder about is whether it would have been possible to test the flap while in orbit, to see if the hydraulic lines were actually ruptured or not.