Because the 12 hour period without screensaver simply reveals nobody was there to close an application (like VLC, iTunes, or a standby). This time lenght reveals that screenplay inactivity cannot be due to human interaction.
Moreover, an even greater problem, is it reveals Bongiorno doesn't believe to her client. Raffaele reported of having dinner, (maybe?) making love, being so high with marjuana to not being able to stay awake and remember things. You cannot "remember" after three years that your alibi instead is different, and consists in being all night actively interacting with the computer (not even with a 5 minutes interruption), this not how it works. If they propose the screensaver log is proof of human activity, this would be like a devastating alibi retraction.
These are only some reasons for why it is desperate, there are others.
Overall, i think also the whole set of their computer arguments reveals the extremly weak position of defence. Those are in fact just arguments on the lacks in written explanations in the Massei report, they are not arguments for innocence. The computer is just Sollecito's alibi, not an argument for guilte, and these are not arguments on evidence.