i think difficulty level is less about "OOOH I CAN WIN DEITY" and more about finding the difficulty with the game-pace that suits you.
Want to build a lot of buildings and wonders?
play prince.
Want to have a shot at wonders, getting "most" buildings?
Your a king.
Want to have about a 50/50 chance on wonders, while having to watch your building maintenance and social policies a little closer?
Emperor, it is!
Want to spend the game playing catchup where the next enemy is ALWAYS around the corner? Immortal can be fun! Despite that your always behind, remember - it's how you finish, and i've won on the bottom of the scoreboard.
Want to dope up with teenage rage and scream at the sky? Well, want a game where you have to make "every right move" without mistakes?
Deity is ok if you want to "play your starter deck against my teferi deck..." just hope i get mana screwed and never draw counters! (trust me, i would mulligan to 4.)
Now, i used to be able to do as bad on king as i do on immortal, once you get "good enough", you can apply most of your current strategy with a little improvement to bump up a level, and keep the same "fun you like" without changing too much. I admit, my plans just don't work on deity but one deity game i built 14 wonders and 0 troops and it wasn't until about turn 200 on normal settings that i got attacked, my poor "One Wonder City"... Maybe if i had taken it seriously and put out 3-4 more cities to meet needs i could have come farther.