What could be wrong with my "save file" improvisation?

The immediate problem is this code here, where you're saving the player as new (and then immediately checking if they're new, even though you've just assigned them to new.) I suspect you're overriding the player's data with the default data within there

Players.PlayerAdded:Connect(function(player)
	playerFirstJoined:SetAsync(player.UserId, "new")
end)

Players.PlayerAdded:Connect(function(player)
	if playerFirstJoined:GetAsync(player.UserId) == "new" then
		...
	end
end)

And the most immediate solution is to instead check if the data is nil (since that's the default value if nothing's been saved) and to assign some other value once they're leaving.

Players.PlayerAdded:Connect(function(player)
	if playerFirstJoined:GetAsync(player.UserId) == nil then
		...
	end
end)

Players.PlayerRemoving:Connect(function(player)
	playerFirstJoined:SetAsync(player.UserId, true)
end)

Now I'm calling these immediate since they're the most direct solution, however, there's some bad design in your code

The problem is that you trust datastores a bit too much. They're prone to erroring if you make set/get requests fast, or just because it feels like it lol. Specifically, you're using another datastore to check if they're new when instead you should take advantage that all their data would be nil if they were new, and also you're making some unnecessary calls to the datastore. A solution would instead to cache the data in the module, which could be saved and retrieved very quickly without worrying about making too many calls to the datastore. Once the player leaves, the cached data can be saved

Players.PlayerAdded:Connect(function(player)
	local data
	local success, err = pcall(function()
		data = playerSaveFile:GetAsync(player.UserId)
	end)
	if not success then warn(err) end

	playerInfo.SaveData(player, data or defaultValue) --Taking advantage of how the or operator evaluates to the second operand if the first is nil (or false.)
end)

Players.PlayerRemoving:Connect(function(player)
	local success, err = pcall(function()
		playerSaveFile:UpdateAsync(player.UserId, function(oldValue)
			local newValue = playerInfo.GetData(player) or oldValue
			return newValue
		end)
	end)
	if success then
		print(player.Name.."'s save file was updated.")
	end
end)

Module Script:

local PlayerInfo = {}

local cachedData = {} --Holds player data instead of making calls to the datastore. You could use this to periodically save every players' data every few minutes or so

function PlayerInfo.SaveData(player, data)
	cachedData[player] = data
end

function PlayerInfo.GetData(player)
	return cachedData[player]
end

Players.PlayerRemoving:Connect(function(player)
	--Cleanup
	cachedData[player] = nil
end)

return PlayerInfo