A TPM is a very slow and dumb chip: It can hash data somebody sends to it and it can encrypt and decrypt data slowly. That's basically it. There is no privacy concern there that I can see. That chip can not read or write memory nor talk to the network.

Together with early boot code in the firmware/bootloader/initrd and later user space that chip can do quite a few cool things.

That code will use the TPM to measure data (create a hash) it loads before transfering control over and then unlock secrets only if the measurements match expected values. There is no way to extract that key on any system with different measurements (like a different computer, or even a different OS on the same computer). I find that pretty interesting and would love to use that, but most distributions do not offer that functionality yet :-(

Using the TPM to unlock the disks is just as secure as leaving the booted computer somewhere. If you trust the machine to not let random people log in, then TPM-based unlocking is fine. If you do not: Stay away.

Extracting the keys locked to an TPM is supposed to be impossible, so you do not need to worry about somebody stealing your keys. That alone makes TPMs very interesting... your own little FIDO tocken build right intomyour machine:-)

I was usimg TPM on my Arch laptop, but then I swizched to a fido device - nitrokey.

I don't care about TPM at all on my personal systems.

In the context of Full Disk Encryption, to this day I don't understand why I'd use it over just typing my password at boot

I wouldn't say using TPM compromises your privacy or security. It can act as an additional layer of protection where your PC boots only when your basic settings are unaltered. You can still have FDE with password and TPM if TPM sniffing is your concern.

Still, I don't use it because I like my stuff accessible and not locked when I dual boot.

Anti-libre hardware

Would like to, but never figured out how to get the TPM 1.2 chip in my X230 to work with cryptsetup. Everything seems to be written for TPM 2.0 only.

Together with secure boot and your own signing keys, it could be a good way to en/decrypt the a dm-verity secured read-only rootfs. But for the home partition I would probably still want to enter my own decryption key, maybe via systemd-homed. From there you can update the kernel/initramfs and read-only rootfs image and sign them for the next boot.

This is complicated to set up. Otherwise maybe use TPM as a 2FA, so you still have to enter a pin?

TPM is not only used by the system encryption. But no i do not use it for it. Not because of privacy, cause of security reasons.