Any attack roll that comes up a natural 1 is an automatic miss regardless of bonuses. I'm playing a wizard and I like my touch-attack spells, and now I have access to wish.
Can a wish be used to eliminate this auto-miss rule?
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Yes, you can wish for it, but you probably won't get it.
A wish can automatically do any of the following:
You are allowed to wish for things not on this list, but the DM is not only allowed but encouraged to twist your wish into something you didn't really want.
Honestly, if I was a DM and someone wished for this, they would auto-miss on 20s instead of on 1s, and be unable to crit unless they had an expanded crit range.
Alternately, when your character plays D&D, the meta-D&D in the game's setting will not have that rule.
Remember, Wish is something your character uses, and your character is (probably) not aware of the mechanical rules the D&D system uses.
Wishes should be worded, or at least able to be worded, in character voice. Since your character is ignorant of the mechanics of his universe, he's unable to voice that wish to affect the mechanics.
As a GM, if a character wished for that, Sure, the character never misses by rolling a natural 1 - in whatever dice games the character plays.
The player still misses on a natural 1.
In the original, pre-edited question, the OP tried to couch the out-of-character mechanics (rolling a 1 5% of the time) with in-character observations ("I summon a bunch of skeletons and cast at them, noticing that despite my superior skill, I still miss ~5% of the time).
The problem with that is that while the miss-on-a-1 rule is a relatively clear-cut and arbitrary "cosmic rule" for the player, it isn't so for the character. It's meant to represent (though not necessarily simulate) the vagaries of the encounter. So even if the wizard keeps a list of 1,000,000 attacks and analyzes precisely why he missed 50,000 times, he will see that those misses were because the skeleton had surprisingly held back for a second, or that he himself had slipped and missed the second between casting or touching, or any number of understandable, realistic and unsurprising in-universe explanations. I don't think you can wish for "none of my enemies will ever move in an unexpected fashion and also that I never miscalculate the distance between us while being fired upon".
But here's a twist: to take the normal course of events in real-life, ignore the regular and observable cause-and-effect and instead infer some sort of cosmic game takes a special mindset. The main problem with that is that if that's the case, then the wish spell is just as part of that cosmic game. It's possible that the gods themselves are, too. A powerful wizard who had gone down that particular rabbit-hole would have no choice, I believe, but to embark on an existential quest to discover what really makes the world tick.
One of my characters made this wish, only she phrased it "I wish that my weapon will always strike true." I dig her flavor text. Copied it down, with the location and how much gold (put in a wishing well for fun sake).
Since I'm DM - I'm thinking she'll get what she asked for. Her weapon won't miss. But the specifics - that's the fun stuff. It could hit her or her allies some of the time, too. Maybe even most of the time, if it's the only one she ever uses. Check out some of the example "cursed weapons," for things such as this. The wish spell encourages the DM to be spiteful because they want to emphasize the "be careful what you wish for." It's just like a character making a deal with an arch-devil - it goes in their favor until the fiend wishes otherwise.
Striving for mechanics, I would make that run badly 100% of the time because it unravels the fantasy feel of the game. If they worded it to 'never accidentally hit their friends,' or 'never drop my weapon' as often happens with a botch, sure they could probably have it. But to tear at the edges of imagination by rule grinding, definite no.
Mechanics-wise, I don't think that wish is unreasonable. I personally try to houserule away the "1 always misses on attacks" rules whenever I get the chance, as I feel that having a 5% chance to automatically miss, no matter your skill, feels kind of crappy. If the player phrases the wish in a way that makes some sense in-game (for example, "I wish that my spells would never fizzle."), then I'd probably give it to them. I mean, the ability to hit 5% more (which is the most that this wish can get you, barring alternate critical miss rules) is absolutely on par with getting 15000gp worth of stuff, or getting +1 to a stat permanently.
While this is most definitely outside of the standard list of wishes, I don't think that a player getting this wish would be that bad.
Can you? Sure. The mechanics of the wish spell, and even limited wish, allow you to wish for whatever you want. But there is some strangeness in the spell descriptions that you should be aware of.
There is a bit of strangeness of wording in the spell descriptions, however. As @thedarkwanderer pointed out in a comment on my original answer, limited wish actually buries the very thing you're asking for in its spell description, though only for one attack per casting. It doesn't get a bullet point of its own in the list of "safe" wishes, but it is explicitly called out in the entry for "any other effect whose power level is in line with the above effects" as an example. At the time of this edit, every answer on this page seems to have overlooked it; I'm only just correcting mine now.
But there is room for some rules-lawyering here, because the description of wish doesn't list it as a safe effect, nor does it explicitly state that it can do anything limited wish can do. I would argue that it would be very, very strange that something would be safe for limited wish but not for wish, particularly since the one-line description of wish in the Sor/Wiz spell list is "As limited wish, but with fewer limits". Even if one were to rule that the effect is not directly safe for wish, you could get it by duplicating limited wish, since the latter is a Sor/Wiz7 spell.
Is it safe to ask for this forever using a wish? Probably not. Since at least 3.0 (and one can argue that this existed in a lesser form in previous editions as well), the description of wish has come with a list of "safe" effects that you can wish for without having to worry about side-effects. If you go outside those bounds, then the DM is free to apply "creative interpretation" or partial effects, or even deny the wish outright, and changing this rule is out-of-bounds on both spell descriptions. @thedarkwanderer mentions the possibility of getting limited wish at will, but I'd be forced to argue that getting a 7th-level spell as an at-will spell-like ability is definitely unsafe, and for that spell to be limited wish would be even more broken.
That said, there are safe ways to reduce the risk of missing. If you've got the resources, for example, you can safely wish to reroll a missed attack: you'll still miss if you roll a second natural 1, but the odds of that happening are only 5%. If you could pay enough XP to cover the cost, you could even wish for a ring that let you reroll an attack 1/day (the psionic power Second Chance has potential as a model for this).
Incidentally, in the interest of game balance, if someone were to try this, I would argue that making an attack automatically hit means that an attack roll is never made. You can't miss, but you can't crit either, unless you're trying to perform a coup de grace (which explicitly auto-hits and auto-crits).
When it comes to things like this I prefer to deny the character his wish and then explain outside of the game why: if I gave it to him that it would make him the perfect swordsman, and perfect does not exist, for if you have nothing to strive for then why take up the sword at all?
However I do not deny the wish entirely and meet the character halfway. For instance, I would suggest to the player they wish for the ability to cast True Strike, and give them the ability to cast it a number of times equal to their INT modifier or some such adaption. Cruel but fair.