I would think that the weight added by another set of tiles would be extremely restrictive.
The space program is not without it's inherent risks. It is a testimony to the brilliance of our scientists and engineers that this type of thing does not happen more frequently. Think about the apathy that this country normally has regarding space flight. (This from a nation that thinks Survivor and Joe Millionaire is exciting.) It shows that those involved with NASA have reduced the risks to the point that it is no longer "exciting" for most people.
Yes this is a tragedy, but it can also be a valuable learning experience for NASA. A lot of safety regulation is unfortunately written in blood. We cannot stop exploring because "someone might get hurt". All that we can do is learn our lesson, put it to use, and move on to a bolder and brighter future in space.
Something else to consider here is that we are discussing all of the possible things that could be done in the event something like this happens again.
But this was only one of many, many things that could have gone wrong. In order to be prepared for every possible contingency on a shuttle mission, or even for every possible contingency that might happen on more than one out of every 1,000 launches, we would be launching shuttles the size of warehouses, with extra tiles, engine parts, engines, wings, escape pods, 5 years worth of oxygen, Florida ballots in case the crew is trapped up there past the next election day, etc.
At times like this it is hard to accept that it is necessary to be clinical about these things, but there are paratical considerations to be made. That's why the speed limit isn't 10 miles per hour on interstate highways.