That’s not how Common languages work though and English is a great example. Modern English is a pidgin that’s developed when old English was dominated by Norman French.
similarly Humans might have been dominated by Elf’s to create a new pidgin language which all humans were forced to speak speak and others pick up as a trade language.
A fair point in how real life language works, but that isn't exactly how things are portrayed in the game.
Firstly, I cannot think of a single world that specifically calls out humans as having been under the subjugation or domination of another race and their language forced to adapt. There aren't even to my knowledge any references to "Old Humanish" as a language that once existed but no longer does, like there is for "Old English"
Secondly, we simply need to look at the PHB section on languages to see that Common couldn't be derived from another language. It is listed as "Common -> Typical Speakers: Human -> Script: Common" while a language that shares a root, such as Dwarvish and Giant, is listed like this "Giant -> Typical Speakers: Giants and Ogres -> Script: Dwarvish"
If common were a pigdin derived from another language, it would share that languages script, not have it's own unique script. Especially since out of the 16 languages listed, there are only 6 scripts.
Thinking of all gods as ‘human’ rather than gods is a bit contrived and if it is protrayed that way in a game thats just lazying DMing really and not something Ive ever really seen.
In the Forgotten Realm I can think of Gond the Lord of All Smiths, who manifests as a gnome and isnt Chauntea a halfling?
I do not know how they are typically shown, but let us take the Forgotten Realms for a moment, because I think this will show what I am talking about. Most of these are from Mordenkainen's Tome of Foes
Tempus is "The God of War"
Bahamut is the Dragon God of War
Vandria Gilmadrith is the Elven God of War
Selvetarm is the Drow God of War
Clangeddin Silverbeard is the Dwarvish God of War
Deep Duerra is the Duergar God of War
Arvoreen is the Halfling God of War
Gaerdal Ironhand is the Gnome God of War
Ilneval is the Orc God of War
And when I did a category sort for "Human dieities" most of the ones who show up are the major gods. In fact, Chauntea shows up as a human dieity, but not as a Halfling Diety. Gond shows up as part of the Lords of the Golden hills for Gnomes on the wiki, but is not listed as a Gnomish diety in the sourcebooks, because his role as "God of Knowledge, Invention, and Smithing" is covered by other dieties such as Bleredd, Flandal Steelskin, and Nebelun. The last of whom is mentioned, because it says in the Wiki that Gond was accepted by the Gnomes as Nebelun, even though they were seperate entities, and only remained in the Pantheon because Nebelun was too busy in other dimensions to correct the mistake.
So, I don't think it is lazy DMing. I think it takes far more work to realize that every single race has a unique pantheon, and their gods are as powerful and relevant as the "defaults" which are constantly ascribed to everyone. I mean, I could also take the gods of Death, because every race has one. Does it really make sense that Sehanine Moonbow, the Elvish Goddess of Death, marks an elf to pass on, hands their soul to Kelemvor, then gets it back to put among their pantheon? Didn't Sehanine Moonbow already judge them? She marked them after all, according to the Mordenkainen's Lore, why is Kelemvor even involved in this? Because he is "The God of Death" for all races, while all races except humans have their own unique gods of death?
Humans are the most adaptable Race so there’s ic reason why they why they are so common across the planet as well as the ooc reason of the players and game writers being most familiar with a human base. I’ve got no issue with that being a base standard, but the whole point of races is to allow for fantastic variation and those are best judged against a human baseline.
I don't disagree with you (except for elves, from what I've seen of older editions, there is an elf for every terrain type you can imagine, sometimes three)
But, I do think it makes for a richer world if every race and culture is given proper space and viewing. Break up the gods into their racial pantheons, and rituals follow. Every race would have different prayers, rituals and stories around death, war, love, ect.
Otherwise, if you keep everyone on the same culture, there isn't exactly a good way to have a "human baseline" culture. If all races worship Kelemvor as the God of the Dead, and they follow his precepts and bury the dead in the way he says, then everyone shares the exact same culture, and that culture is human. And if everyone is human, there is very little variation.