Why is this? If my computer gets stolen all anyone needs to do is crack my password and they get my coins. I want to remove any trace that Electrum was ever on my computer. Can somebody tell me how to do this please?
If you want program Electrum (or another) to not leave traces on your PC, then use Tails OS. Tails OS is installed on the flash drive from which it is loaded and all files are automatically deleted after completion of work (reboot or shutdown PC). You don’t have to manually search and delete anything on your PC, so as not to leave behind information that is important to you. Tails OS is also pre-installed with Electrum.
Also if I forget my seed phrase, I'm sure I'll also forget where I stored my super-secret titanium copy. The worst scenario is that I get knocked on the head and forget who I am, but then do my coins mean anything to me anyways? Plus with memorization I can travel world-wide without customs asking me what is this weird little electronic device in my pocket or this note with 12 words on it.
It is unlikely that customs will pay attention to a flash drive (with Tails OS), so you can take it on your travels.
It seems to me that it would be more reliable to have a (physical) backup with the seed-phrase in a safe location in case you forget or you "get knocked on the head". It's even better if a trusted person has access to the seed-phrase and can pass it on to you when you're traveling, although this does create additional problems. I think that relying on memory alone and not having backups is reckless. Not to carry with you, but in case of need for restoration (keep in a safe place).