Also FDE is not available to a lot of the Electrum users, basically it only helps Linux users.
Bitlocker is available for free for certain versions of Windows. Veracrypt is a pretty well maintained fork of the old truecrypt codebase, I believe it has FDE. There are also many commercial alternatives, symantec has a well known FDE product. Also EFS is supported by all versions of Windows that use NTFS and will let you encrypt certain directories.
I'd say the only people who don't have access to many FDE options are Mac users. There are plenty for Windows/Linux.
Even if users used the same outer/inner password, it would still be equivalent security to the current version
Nope, because if you had your wallet open and someone got hold of your PC, they can grab the password from your RAM and spend your money. This can be done even if the attacker only has access to your PC for a few seconds. The first and second passwords MUST be completely different and you shouldn't rely on the first password to provide any kind of protection. It's purpose should be to prevent against casual snooping ONLY and NOT to secure your funds, and the user should be made aware of that.
I could probably guarantee that at least 20% of wallet users would use this feature if it was available. You don't lose anything, you simply gain additional privacy it's really a no loss situation. It would even be fairly simple to implement in, just encrypt the public/tx files, and add in a password prompt (if enabled) at startup to input the key to unlock the files.
I agree with ThomasV that if used wrong by a user it will make them significantly less safe, but I do think it is a useful feature nonetheless.
The software should check to make sure the first and second passwords are different. It should show a message informing the user that the first password should be ONLY relied on to protect privacy (casual snooping), and the second password is the one that actually protect your funds and warn the user to use two completely different passwords.
It should also be possible to recover the funds using only the second password in case the first one is forgotten. This could be done by encrypting the seed and private keys with the second password, and encrypting labels, transaction history and previously used addresses with the first. If the user forgot their first password, they would be able to access their wallet with the only the second password but would lose their labels.
I think an implementation like this would be a good compromise. Maybe someone could implement this in a plugin or something.