(This does mean a +2 sword is almost balanced with a +1 flaming sword dealing 1d6 fire damage with a hit. Coincidentally what 3e had for magic item design.)
Yes, and so a +1 sword is balanced with a +0 flaming sword...
3e decided that it must be assumed a lot about what magic equipment the PCs should have at various levels. For example, 3.0 even had DR based on the number of +s. It works, if you accept what is essentially a gamestyle assumption on availability of magic items, for others it sucked.
If most magic weapons have a + as a baseline, this means that in a campaign using magic weapons (i.e. the majority) all weapon-wielding PCs have an additional +1 by default. If this is considered small, then we don't need it. If this is considered significant, then it's the same mistake as in 3e, albeit smaller in magnitude.
This is a matter of taste. Simple works for some people. Sometimes people don't want an extra power.
Plus, again, without simple magic items the ones with amazing at-will powers don't feel as special. They become the baseline and you have to make even cooler magic items to award something special.
And not every game has the same level of magic. Many settings make lesser magic items common; Eberron for one, and Dragonlance and the Realms both seem rife with minor magic weapons. In those cases you want a simple magic item that's still magic but not not a flaming sword of fire.
In my experience, even a +1 longsword can be special if it is presented as being special. If it's just "here's a +1 longsword" it will always be lame, but if you say "here's Ice, forged of Valyrian steel over four centuries ago during the Age of Heroes." then the sword will be special and memorable even if it is just +1.
I am totally not following you... I agree on all these things, and yet I can't get why you come to the opposite conclusion as mine.
Yes it's a matter of taste > and this is why I don't want to see the vast majority of example weapons with a +, but rather a minority (it doesn't have to be none at all, I just want this to be not the most common case).
Yes sometimes people want simple without an extra power > and this is why I think most weapons with a special ability should not have a +, and viceversa (and some have both, but the minority). So if I want the extra power only, I don't have to get the +N (note: it might feel it's free to get the +N, but normally it's not... you could have bought/found/crafted 2 items instead of the one which carries a bonus you didn't ask for)
Yes, without simple magic items the others don't feel special > but also if all weapons come with a +1 on the side, then having a bonus-to-hit never feels special either.
Yes, +N items can be special in their own way > in fact I'm not saying that I don't like +N items in the game... I'm only saying that I don't like that "+1 fries on the side" to almost every magic weapon. It just creates a "+1 floor" to all magic weapons which is not useful to the game (either it's too small, or you will adjust all monsters accordingly), and possibly makes it even more difficult to let those +N simple items feel good.
EDIT
One last comment...
Let's always keep in mind that magic items in 5e are supposed to be optional, but it's reasonable to think that the vast majority of gaming groups will at least use SOME magic items.
The magic items in the DMG are just examples that can be modified, but still a lot of groups will use at least some of them as-is (at least when they are just starting off playing the new edition).
Because of these, I think it'd be best if the examples presented will be as varied as possible without setting "trends". Right now, the majority of weapons carries a +1 for no other reason than tradition (notice -> not the majority of armors! so the reason cannot be to represent masterwork compared to the mundane counterpart), therefore sets a trend. Tradition is good, but IMHO in this case it's just a burden.