Let's not make this into YGO please. EtG has it's own charm, and one thing about it is that it differs from some of the other big card games. I don't know about magic, but it's much different from YGO in that it uses quanta, no sacrifices, no creature to creature combat, and no traps; the last point makes the game have a unique and calm feeling when it's a player's turn as they know they are safe. This is also the reason that EtG doesn't utilize a graveyard.
The only way this concept could be done and done well was if a large amount of it got added into the game, but if more cards and mechanics are to be implemented, I can think of hundreds of others that would benefit the game more.
This also depends on how traps are implemented.
YGO made trap triggers for just about any and every effect type possible. So I do agree, it goes a little overboard there. It doesn't mean the concept can't be adapted uniquely here.
I see no problem with making trap cards that trigger against the opponent using single target effects that target something that isn't theirs.
Players are still "safe" on their own turn. Its their choice whether to target something owned by the opponent or not.
If they do so and get burned by a trap, its their own fault targeting something that isn't theirs without knowing what it was first.
A great example would be allowing a player to play a voodoo doll facedown... If your opponent shoots it with an ice bolt and consequently takes damage and freezes their own weapon, then they'll think twice about firing at facedown cards without knowing what's there...
In fact, that would actually be a good way to get the voodoo mechanic to see a bit more use outside of very specially designed decks.
I.e. I think traps should be just fine as a "defensive" mechanism.
On the other hand, making traps that trigger if opponent plays a creature to their own field, casts a healing spell on their own creatures, etc. Would be much more invasive...
Personally, I wouldn't really mind too much since it adds a much more cereberal element rather than the very simplistic shotgun style play. But I can also see how some may dislike that as well.
So using traps with "offensive" mechanisms may detract from the current overall feel of the game for some players.