In response to a few things:
- 'they generally don't look good' is I suppose a matter of opinion - but I do like a number of them myself, and many other fans have some normal types as their favourite Pokemon.
- 'their stats aren't too good' however is where I have some qualms - it seems you are forgetting about the likes of Snorlax (who was a beast in the older games as well and still used), the Porgon line gets pretty decent usage as well, Slaking has one of the highest attack stats (ignoring its admittedly terribad ability it can still hit very hard in a hit-and-run style), Togekiss has a lot of special attack and special defence and Blissey's huge HP stat puts it at the top in that regard...
and comparing to the other Pokemon they slot in the top 100 with a number having upwards of 530 Base Stat total. They even rate higher than the starter Pokemon in terms of stats and the majority of Pokemon beating them are Legendaries (and let's not forget the one of the top (Arceus) is a normal type himself). Like every other typing in general, there's those with bad stats, but also those with good ones.
I'd argue that the fact they don't have any advantages over anything with STAB moves (a lot have a rather varied movepool let's not forget) is potentially purposeful and the 'point' given the are the 'Normal' type as well, but that's my take on it. =p
As for the thread topic... no, I wouldn't change any types nor add another. The system works more or less now since the changes in 2nd gen (which were only done to fix the hug imbalance in gen 1!) and after so many years of Pokemon canon, to decide that these Pokemon are now ____ typing instead of what they were established as seems rather silly and pointless to me - and changing how the typing system works could arguably make it worse. (Then there's the changes to how Hidden Power works which runs off the IV system...all in all you've got a potential mess waiting to happen by removing or adding a type).