This is a tough topic to discuss but needs to be addressed...
First an explaination of terms used here:
"disc authentication" refers to the generation(by the CC hardware) of the PS1 and PS2 protection signals which are normally embedded in an uncopyable form in official discs.
"firmware" refers to the small bits of code which are stored in an upgradable EEPROM on the CC PCB. these bits of code are responsible for controlling the behaviour(what it will/will not boot, etc) of the CC and the PS2.
"homebrew discs" refers to discs which contain unofficial software, such as emulators, demos, etc. These discs must contain files with specific names so that the CC firmware may determine that these are allowed to be booted.
Now, on to the answers...
Crystal Chip is a well designed chip with many advanced capabilities. The CC has the ability to authenticate discs regardless of the content of the disc(homebrew, backup, original, import) so that you may access them as if they were legitimately pressed PS2 game discs. It is the CC firmware which specificially blocks the booting of all discs other than original non-import discs and discs containing homebrew software. Due to limitations in the PS2 architecture, there are very few ways that CC can go about determining what types of disc are homebrew.
Take PS2 discs for example. When you boot a PS2 game disc, the CC firmware will check if this disc is a "homebrew" disc. It will determine that it is not a homebrew disc and turn off the CC disc authentication and force the PS2 to re-check the disc authentication. If the disc is an original non-import game, the disc will authenticate itself as it would in a non-modified PS2. The CC firmware will then boot the disc. If the disc is a backup or import, the console will not allow it to authenticate and therefore the CC firmware will not be able to continue booting the disc.
The CC firmware software is open-source, meaning that you can freely download and change the firmware to suit your individual needs(provided you have an understanding of MIPS assembly language). This allows people to do things with CC that we hadn't thought of or things that we cannot allow by default due to legal or moral reasons. We understand that some people do use modchips to play legitimate backups and import games, but the laws in various areas of the world do not necessarily protect your right to do so. We also do not wish to further the damage that piracy causes to the software industry. That being the case, we must do everything we can to prevent our product from being labeled as a device which allows you to break laws so that it may be enjoyed by everyone everywhere.
In the end, it is impossible to stop people from playing backups on their PS2 as Sony themselves have found. So the answer to your question is "yes", it could in theory be modified to allow the booting of all media types.
This is the only discussion that will be allowed on this topic on this forum. We do not wish for people to focus on booting backups and such as this is not the intent of CC. CC is intended to allow you to do what you want with your game console. The user is the one who must decide in the end if they will do the right thing and buy software, or be stupid and steal it. Please be responsible, don't abuse the freedom of choice that modifying your console gives you. Buy software and support the game industry. Without them, we'd all be forced to play board games.