You are correct with your assumption that there is a "double-encryption" occurring. This of course has the result of causing a lot of drive thrashing to occur. Having previously had to fix numerous corrupt FileVaults, I would first back up the sparsebundle. Once that is complete, I would then disable Legacy FileVault.
Ultimately, the only real reason to maintain this setup is if there is reason to suspect there are others who possess login credentials (especially admin credentials) and are capable of mischievous behavior. Even under that scenario, my recommendation would be to encrypt the files which need to be kept secret using TrueCrypt and disable Legacy FileVault.
Mount the Time Machine drive / volume on your desktop and navigate to the snapshot you used to restore the Mac.
In the /Volumes/path_to_tm/Backups.backupdb/Mac_Name/Latest/HD_Name/Users folder, you will either see a directory or a file.sparsebundle named for your user's short name.
If you see a .sparsebundle, you had FileVault 1. If not, then not.
The answer here also depends on which version of FileVault (1 or 2) you were using on the missing Mac.
FileVault 1 is based on encrypting just the home folders of accounts as opposed to encrypting everything on the Disk. If you enable FileVault in OS X 10.3 - 10.6, this is what you get; upgrading to 10.7/10.8 will leave the encryption intact (now called "Legacy FileVault").
If you recover an FV1-protected account, the encryption should be maintained. Since your recovered account is not encrypted, you didn't have this enabled on your account on your old computer.
FileVault 2, on the other hand, is based on encrypting the entire startup volume -- all accounts, the OS itself, etc. If you enable FileVault in OS X 10.7 or later, this is what you get. You can also "upgrade" from Legacy FV to FV2 by disabling Legacy FV, then enabling FV2 (note that Apple recommends doing this, but it is not automatic).
If you had FV2 enabled on your computer, there's no way (at least, no easy way) to tell from the backup. 10.7 and later allow you to encrypt the backup, but that's independent of encryption on the startup volume (i.e. it's entirely possible to have an unencrypted backup of an encrypted system, or an encrypted backup of an unencrypted system). Also, the restored account will be unencrypted, unless you specifically enable FV encryption on the new computer.
Best Answer
Just go to System Preferences, click on Security, then FileVault then click the button that says turn off FileVault. But if you have it on, I would recommend leaving it on. It increases your security, and may take a while to turn off (decrypt) your files, but it's your choice.