Tempered Glass For Cookie Sheet
I could see two problems. First, glass isn't very thermally conductive, and it has a lot of thermal mass, so it might take quite a while for the glass to heat up, especially if the glass is thick. This means that you might not get the bottom/middles of your cookies cooked properly; if it takes long enough, they might just dry out.

Second, while tempered glass is made to withstand "reasonable" impacts and temperature changes, what you're describing may not be "reasonable", especially if the glass is thin. The corners and edges would heat up much more quickly than the center, setting up serious stresses. Too rapid a change, or too thin a glass, and the whole thing might shatter.

There may be a magic thickness which neither shatters nor slowly dries your cookies. I won't be doing the experiment; let us know if you do.