That's how it has worked in AD&D and 3E. This allowed the spellcaster to throw in more spell resource to the fight, which can be good and bad (good = being allowed to play the resource game, bad = driver toward 15-min-workday).
Whether or not it works in 5E depends on how you interpret the word "once" in the text "Once during each of your turns, when you take an action, you can also move the hammer up to 20 feet and repeat the attack against a creature within 5 feet of it."
If the "once" applies in general, then you can only attack with one Spiritual Hammer per turn (or in a round where you cast it again, you would attack twice, but then you'd always have one unused hammer hanging around).
If the "once" applies to each casting of the spell, then yes you can have multiple.
Now I'd like to take the "once" equals once in general approach, and limit use of the spell. However, I suspect that limitation will be disliked by most experienced Cleric players, who would mostly like to have it work the AD&D and 3E way. Not that it was that common to see 2 or more on the battlefield in practice in my games anyway, so it's mainly academic . . .