{be} starts a new chain. {bei} continues the current chain. {be'o} terminates the current chain. Technically it is somewhat extraneous, but working the other way would require you to fully terminate the last sumti in the chain, so that a new {be} could only attach to the old one. This could get quite verbose if the previous sumti was complicated.
For an artificial example, {mi tavla be* fi lo nu mi'o klama lo zarci kei ku be* fe do}, where be* is this modified {be} you are considering. The {kei ku} cannot be omitted (though {ku ku} would have worked). Compare this to {mi tavla be fi lo nu mi'o klama lo zarci bei fe do}.
mi'e la latro'a mu'o