Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
It might be weird to say that this book—being old, adventure-ridden, and full of crazy intrigue—doesn't follow a "classic plot." But it doesn't.
Sure, we have a beginning and a end. And they tick all the boxes of a "beginning" and an "end." In the beginning, there is chaos; at the end, there is death and a happy deliverance to Heaven.
But the middle bit? Well, the conflict, complication, climax, suspense, and denouement are all sort of rolled into one. This is for two reasons.
The first is because this is kind of a picaresque novel, where the main character just roams around and meets people (think On The Road).
The second is because The Pilgrim's Progress is, in no small part, an attempt of John Bunyan's to convert people. He wants to throw in a ton of action that shows people that whatever kind of lives they lead, they too can be Puritans.
So he keeps the body of the story kind of muddled. This is a smart move—the middle bit of a story coincides with the life of a person. We all are born (initial chaos!) and we all die (conclusion: womp womp) but our lives become individualized because of what happens in the middle. So Bunyan is keeping this story applicable to all readers by not adhering to "classic" plot.
Initial Situation
We are confronted with a mysterious image: a man standing alone, distressed, with a book in his hand, and saying "with a lamentable cry," "What shall I do?" (P1).
Who is this man? Where is he? Unlike most stories, this one doesn't begin by explaining the situation or letting you know where you are. Since this is an allegory, in a way, none of that matters. What does matter is the emotional situation and that's what Bunyan confronts you with in this image of his protagonist, Christian, before he even has a name.
In the next few paragraphs, we learn that this distress is due to the impending destruction of his city (conveniently named the City of Destruction). Christian is desperate—desperate enough to leave his family (never a crowd-winning move)—and follow Evangelist's vague advice to go find the Little Wicket Gate. Here, Bunyan is saying something about the way that journeys toward salvation begin: with a deep, body- and soul-shaking conviction that something's wrong and a willingness to go against the tide (and one's own preferences) to change things.
Conflict / Complication / Climax / Suspense / Denouement
The Pilgrim's Progress is structured with a one-conflict-after-another dynamic. This also, of course, is a part of Bunyan's message about what the Christian life entails—one conflict after another—and the danger of ever thinking the worst has passed.
Christian has guides for what he should do and where he needs to walk to get to his destination, but the real-life obstacles he faces often complicate this knowledge. Because he's a human being, not just a concept of a "Christian," Bunyan's hero still has very human needs and temptations.
What all of this means is that a clearly rising and falling plot would be at odds with what Bunyan is trying to show: the nature of being a Christian in real life. The fact that there are so many mini-plots in this story shows that the more Christian goes through, the more faith he can have that things will turn out fine. This is Hopeful's logic with him at Doubting Castle. Because they have survived so much already through their faith, how can this one challenge defeat them?
So you see, there's a way in which the episodic, non-conventional plot structure is Bunyan's means of simulating the real-life experience of faith—its challenges, victories, and simple days of plugging on—in the experience of his reader.
Conclusion
It's hard not to think of The Wizard of Oz as the pilgrims finally reach the Emerald—or Celestial—City.
Like any great journey-story, the goal is surrounded by an aura of awe and charm. After a story-long (or in this case, remembering the allegorical mode, life-long) struggle, the destination seems all the more fulfilling because of the way we've longed for it. The pilgrims' arrival at the Celestial City is the perfect example of this.
However, remembering that this is an allegory, it's also a bit more complicated. See, facing the river in front of the gates, Christian and Hopeful are really facing death. As their last "challenge," crossing the river means getting through the pangs and fears of death without losing faith in God. The fact that death is just a river that they wade through, though, really emphasizes the continuity of life into the afterlife.
The final vision of Ignorance in the conclusion also highlights this. Poor Iggy is forbidden from the city because of how false his devotion to Christ was in life. In this way, passing through death with faith may be the final test of a Christian, but it's an exam that he will have been studying for his whole life—if he's really doing the whole Puritan thing right.