Honestly, at this point I think Normal is kind of an unessacry type outclassed by pretty much every type in a niche. Offensively, Normal is outclassed by Flying, which hits Bug, Grass, Fighting super effectively, while Normal does not hit anything super effectively. Both are resisted by Rock and Steel, and is resisted by Electric for Flying and an immunity from Normal for Ghost. You could say that they are on par for neutral coverage, but Flying outclasses Normal in terms of Super effective coverage, so Flying will be the better choice in terms of coverage for the majority of Pokemon. This comparison is really important, since Flying/Normal is by far the most common pairing for Flying, but if we were capable of removing the Normal Type, it Pokemon like Pidgeot, Braviary, and Staraptor could function mostly unchanged. That being said, Normal/Ground do pair well with each other, but there's only Diggersby with this distinction, and other Ground Types can't really take advantage of this coverage because Normal does not hit anything super effectively. So aside from STAB, Normal gets the award for the worst type for Super Effective Coverage, only being beaten by Dragon.
Defensively, It only has one weakness, which gives it this distinction alongside Electric. However, yet it only has one resistance, an immunity to Ghost. This is valuable considering, that Ghost is one of the best offensive typing due to only having Dark and Normal resistances. However, despite having an immunity to Ghost, they cannot offensively threaten without relying on a coverage move, which makes them much weaker checks in comparison to Dark types. That lack of an effective coverage option can even invalidate them as Ghost Type check at certain cases.
More on to Aethstics, I definitely agree that the Normal type is definitely the outcast of the types.
Codraroll already explained it, but to show how generic the type is, it's the only type to date to have
lost Pokemon, losing several when the Fairy type was introduced. It's probably just easier to remove Normal since its quite generic in typing. Also worth noting despite Normal types having wide move pools, most of them really couldn't take advantage of it due to having abysmal SpAtk, in fact, Normal types on average have the lowest Sp.Atk of all fully evolved Pokemon.
Celever brings up the sound moves, but the majority abusers happen to be those with the -ate Abilities. Speaking of the -Ate Abilities, Normal is the only type to have such interaction, probably because its the most "basic" type among the types themselves.