Several chapters of John don’t make sense if you read them as being chronologically; Some authors have proposed that what exists as a single gospel was once a collection of readings, compiled immediately following John’s death, or, given the closing curse to do those who would add to it, anticipating John’s imminent death.
If you take John 1-2 as chronological, you actually end up with a big problem: John is baptized in the Jordan a few weeks before Passover. March is not an ideal time for taking a dip!
But moreover, John 2:13-21 is as closely paralleled by the synoptic gospels as any passage in all of John. And the synoptics place this event as immediately before his final entrance into Jerusalem.
I agree that harmonizing chronology between John and the synoptic Gospels is difficult, but that’s not the same as saying, “Nothing in John’s gospel suggests it is chronological.”
Many things in John’s Gospel suggest is it chronological, including the basic narrative. Putting the four Gospels together is difficult, but it’s not because John has said, “Hey, reader! I’m doing a post-modernist random-sequencing thing, knock yourselves out!”
I would say that John’s Gospel implies chronology, just as the others do, because they are narrative texts. If they don’t easily match up for us, that’s our problem, not the Evangelists’.