Bible uses the future tense. Your speculation its extinct is not biblical. Bible does not say Leviathan will go extinct, it says it will be killed by God with a sword.
I like your approach to this subject.
Okay, let's go with Leviathan still alive and well on Planet Earth.
In that case, are you assuming that, just because it hasn't been seen recently, it no longer exists?
Do you think that's the proper way to approach this subject?
How do you know, for example, that somewhere on the earth, there are people who actually live their lives hunting and/or being terrorized by these things?
In the movie
Close Encounters of the Third Kind, I remember a scene where investigators went to a small town, where the townsfolk were going out regularly to watch a UFO land.
It had been landing nightly, or something like that; and was quite an attraction to the townspeople.
And if my memory serves me correctly, they were taking lawn chairs, sack lunches, and whatnot out there nightly to see their UFO show up.
Let's not put all of our eggs in academia's basket and assume because they haven't found Leviathan, Leviathan doesn't exist.
Remember the Loch Ness Monster?