Okay, but, aside from Dwarves getting an assortment of axes and hammers, and elves getting a couple of sword/bow/crossbow proficiencies based on sub-type, that's not really a thing in 5e. Halflings do not, for example, get any kind if innate weapon proficiency. Outside of that, you get your proficiencies from class, and so if you're a cleric, as you suggested, then you have at least all simple weapons to choose from...
So, I'm still really not seeing anything at all that would even remotely suggest that
This is exactly what I mean about missing the nuance of D&D, no halflings on their own do not have weapon proficiencies, but their traits mean they suit some classes more than others and so have a natural aptitude toward certain weapons proficiencies that come from class, I gave the rogue as a perfect example.
It is possible to create a melee Cleric at higher levels [...] though you are limited to bludgeoning weapons such as maces, etc.
That's feel like you're pulling it out of a personal conception/stricture that really has no grounding in anything (except possibly some rules in older editions that have rightfully been discarded by now), as far as I can tell.
You can favor whatever weapon you like (usually one favored by your deity if you're a cleric), within the simple weapons group, as well as any weapons you happen to get from your race or background... there's nothing at all restricting you to bludgeoning damage choices.
Not at all, Clerics have for a long time throughout D&D history had a warrior style which was later further developed into the Paladin class, but the traditional warrior cleric is still very possible and that's even before you consider multiclassing.
There is a wealth of warrior cleric D&D fiction out there and many a campaign including them.