Where does it say things are automatically detected? What is the point of detect spells?
Where does it say that an invisible creature is hidden? Given that hidden and invisible are two conditions which the rules actually care about, and they are distinct from each other, the rules can reasonably be expected to specify if applying one would typically also apply the other. Unusual circumstances may change that, and that's why we have a DM to adjudicate, but the rules listed should be sufficient for typical use.
It's like of you had a spell that pushed someone back twenty feet, but didn't specify that they fell prone at the end of it. Some people might imagine that being thrown back twenty feet would cause someone to fall prone, but if that was intended for normal situations without some sort of mitigating circumstance, then the description of the effect should indicate that. Likewise with a spell that deals fire damage; barring situations where the target was
unusually flammable, it's reasonable to expect the spell to specify if it should normally set people on fire as a result of basic usage.
The condition also says "a invisible creature is impossible to see without the aid of magic or special sense". If there is any doubt the heavily obscured section talks about the blind condition, so against the invisible thing people are blind.
Yes, an invisible creature is impossible to
see. That part isn't in dispute. The contentious part is - apparently - that you don't need to
see something to
know where it is. Sight is overrated, according to the rules, which is why invisible and hidden are two distinct conditions.
It also says the creature's location can be detected by noise or tracks, obviously an invisible creature is not detected by default as you say, it's logical, sight is the only targeting sense humans have and this is translated to the game.
Given that this is the only time I have
ever seen anyone use the phrase "targeting sense", I'm going to say that it's not the obvious chain of logic that you seem to think it is.
The DM determines the DC as always, I don't see the problem there, for example if you are seeing a parade or a concert you should not be able to hear any footsteps, if there is people moving and talking it should be very difficult to discern the noise of all footsteps, if the creature walks silently then the difficulties should rise, if the floor makes noise it should be easier.
The difficulty of detecting a hidden creature is based on its Stealth check, which it hasn't
rolled if it didn't take an action to hide. Modifiers may apply due to circumstances, sure, but the Stealth skill of a target is always the primary factor. That's the mechanical irregularity which would be introduced here.