Because he's a moron.
Well, that's a bit harsh. It would be more accurate to say that Scamander falls into the "absent-minded professor" role. He knows a great deal about magical creatures ("book smarts"), but lacks basic awareness and common sense ("street smarts"). This is a standard character archetype which you will see in many different works of fiction. The story is largely about Scamander growing and becoming a more rounded character. The quest to recapture all of the creatures is a vehicle for this character growth:
- During the bank scene, it becomes painfully obvious that he had no plan whatsoever for any of his creatures escaping. He simply did not expect this to happen at all.
- In the scene with the Erumpent, he displays a greatly improved ability to improvise, but is still largely relying on book rather than street smarts. We see the same thing during the department store scene.
- The escape from MACUSA marks a shift: Scamander's situational awareness is greatly improved and he is able to act adroitly and independently.
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By the end of the movie, he is able to identify an undercover Grindelweld largely on intuition and an offhand remark by the latter.
At the beginning of the movie, Scamander simply does not have the common sense to realize that his plan is fragile and unlikely to succeed. His creatures come with him across the Atlantic, not because he planned it that way, but because he failed to make alternative plans for them.