Just remembered that I have written the recovery seed phrase of my Electrum on a piece of paper somewhere in my place. I'm wondering what could go wrong since my place isn't too secured.
Your priority should be to secure your home. Not just because you own bitcoin and have a recovery phrase somewhere in it, but because both you and your belongings are vulnerable if it isn't secure. What could happen is that someone breaks in easily if it isn't safe and steals your valuables.
How about trying to memorize it? Is it possible?
It's possible, but that shouldn't be your only backup. You should have multiple physical copies of your seed, preferably in different geographical locations. After that, you can try to memorize the words just to see if you can. Obviously, you shouldn't write it down and leave copies all over the place to see if it's still in your memory.
Would you try?
I have never tried it. I remember parts of my passphrases, especially those I use more frequently. But my recovery phrases are hidden and this isn't something you need to access all of the time unless you are recovering your wallets or using stateless signing devices.