The threadmill of earlier editions where you went from +1 to +5 (or +6) weapons, armor (shields and ammunition) never was a big success in my eyes and not something 5e needs to repeat. Fewer, more significant items something I think will work out well.
The odd thing about +1, whatever the edition, it means a 5% better chance to hit. That's a bigger deal then many people think. How many times do you miss by 1? (as a DM, I only miss by 1 if it means CERTAIN DOOM for a character who has been battered unfairly by the dice already. Otherwise, I never miss by 1. Drink.).
Anyhow, 5%s can add up!
5e bounded accuracy suggests not to shell out weapons higher than +1 with ease.
However, the worst thing about + weapons is not the bonus itself, but rather the effect (seen in previous editions) of turning them into currency. In previous editions, +1 weapons (and other common items like cloak or resistance, ring of protection...) are a standard at a certain level range, all NPCs have +1 weapons at some point, and the PC soon each have their own and end up treating all the excess +1 weapons as money i.e. sell them and buy what you really want. Unfortunately, 3e with its built-in wealth-by-level system, almost requires all NPC to have weapons with +s appropriate to the adventure level.
Now if they want to stay safe with bounded accuracy in 5e, they are going to have only +1 weapons in printed adventures (with occasional exceptions). This may seem better than 3e, but from some point of view it might be worse, because now there isn't even any diversity after the first few levels... do we want every single NPC after e.g. level 3-4 to have a +1 swords? That means, soon the PC will find so many +1 swords that it's even more a standard currency than before.
That's why I said I'd rather
never have published adventures give out +1 weapons.
It would be so much better if printed adventures only contained major magic items related to the story, or minor non-bonus trinkets. Let the DM then freely pour additional magic items into them, and take responsibility for the mess.
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Note also that the old 'magic as technology' approach doesn't work well with bounded accuracy.
When we had weapons up to +5, we could have a fantasy world where higher +s corresponded to higher technology skills: every town might have someone capable of enchanting +1 weapons while maybe you'd have to find someone important to get a +3, and perhaps only a handful of people in the whole world could make a +5.
Now that anything beyond +1 already has to be kept in check because of the math, technology diversity is only between +0 and +1. It's not that interesting as technology anymore.
We can still have 'magic as technology' for wondrous items and other non-bonus items of course.