The Wish spell is a super powerful spell, that can do many things. But if I say,"I wish that this dragon is dead!" or something like that, does it die? The spell description does not say in favor or otherwise.
Yes, using Wish to wish someone dead is possible and is even presented as an example of a "custom wish" apart from the bulleted suggestions.
However, it is specifically listed as an example where the Wish might not work as the caster intends. Terms of fullfillment of wishes are up to the DM - the spell description states that wishing that a villain was dead might simply time-warp one to future after the villain's passing. The DM can also come up with other ways to make the target dead without effectively killing them, like turning them into a nonliving but equally powerful creature.
So, while the target actually dying is an outcome the DM can give, Wishing something was dead is not a reliable way to kill it.
Normally, a spell in D&D doesn't do something, if there is another spell of same or higher level that explicitly do the same thing. For example, Dispel does not remove curses, but Remove Curse does.
There is Power Word Kill spell that does exactly what are you asking for:
You utter a word of power that can compel one creature you can see within range to die instantly.
Wish description says you can duplicate a spell effect, but it has an important restriction:
The basic use of this spell is to duplicate any other spell of 8th level or lower.
You can't duplicate Power Word Kill since it is 9th level.
The Wish description itself have an example how "I wish this creature were dead" could fail:
This spell might simply fail, the effect you desire might only be partly achieved, or you might suffer some unforeseen consequence as a result of how you worded the wish. For example, wishing that a villain were dead might propel you forward in time to a period when that villain is no longer alive, effectively removing you from the game.
The exact outcome is up to your DM.
Being quite broad with your wording like that can be dangerous. "I wish it was dead" can be interpreted many ways. The book example states it might send you to a point the future when the enemy had died. Not recommended.
However, if you made the wording more more specific, I'm sure you could come up with ways to kill it rather effectively.
There's a lot less room for DM-interpretation if you say something like "I wish that dragon had a fatal heart attack" or "I wish that dragon's blood suddenly turned into gold" and lets be honest, if the DM still lets it survive that through the wish adapting it's biology, you still get to kill a dragon and have all of it's blood be liquid gold. You're gonna be rich.
So yes, it is viable to kill someone with the wish spell, just keep in mind the lengths to which your DM may go to bend the interpretation of your wish, depending on how badly you're about to ruin their campaign. I would also note that if instead of casting the wish yourself, you're getting the wish from a sentient creature, like a genie, you also need to worry about how the DM is going to interpret the wording of your wish from the view of said malevolent creature, such as
"...The Halfling, overjoyed, wished for immortality, so the Marid polymorphed him into a fish that flopped around humorously until, finally, it expired. It's a cautionary tale that has survived through the ages, so I suppose the Halfling got his wish." (MM, 146)