I have read much about the Telecaster, but I still don't know what Leo Fender was thinking. I know that Seth Lover was thinking the same thing, as PAF humbuckers had covers too. It was only into the 70s when you started seeing pickups with their covers removed. Even Strat pickups are covered, albeit with plastic.
In part, the nickel cover was to make the guitar look better. The bridge pickup isn't covered, but the original design had a chromed cover for the whole bridge. Because guitarists wanted to be able to do things like palm muting, they were generally left off -- Albert Collins is the only guitarists I can think of who used one -- and were used as ashtrays enough that they're called "ashtray bridge covers".
Part of the logic could be the same as the piece of tape on the treble side of Steve Vai's EVO guitar, that a string could get caught in the bobbin and might hurt the windings, but that seems unlikely because it was only in the 80s with the Floyd Rose tremolo that an errant high E could even get there.
Some have removed the cover, and some pickup makers use covers with cut-off tops. The reported effect is brighter tone and more clarity.