First, I want to point out that flying characters already had this option at the cost of a single feat, Flyby Attack. Flyby Attack is different from Spring Attack in that it allows any standard action during movement, which is massively more valuable.
So this would eliminate the point of a few feats, like Flyby Attack and Spring Attack. But I have played in games where Spring Attack was explicitly changed to work like Flyby Attack (rather than being a single attack only) and had its Dodge and Mobility requirements waived, and it still didn’t get taken by anyone. I have also played characters that did take it, because it was required for something or other, and... it didn’t really matter.
In the end, positioning just isn’t that important in the d20 System (unlike, say, 4e). Ranged characters don’t have particularly stringent demands on where they stand, and melee characters typically don’t want to leave melee once they’ve closed.
So the only cases where it ends up mattering a lot are:
your melee attack kills, so you want to move on to the next thing. Ultimately, to have your one single attack be the difference isn’t that common an occurrence, and you can always just charge next turn or whatever. This can actually hurt you if you move into melee with your next target, but cannot attack – now that target gets to attack you first, without even having to move. Bad news bears.
making the difference in an otherwise-symmetrical situation (move in, attack, move out). Unless you foresee a lot of literal mirror-match one-on-one duels on featureless terrain, usually some other factor is more significant.
you have truly massive movespeed and the room to use it, and you have powerful ranged options (read: spells). By which I mean more than double that of any of your opponents. That’s pretty hard to get, and usually costs too much. But it does make a big difference for, say, dragons..
Personally, I say go for it. It offers a few more options, it seems a little more sensible, and the loss of these feats as meaningful choices is minor; they probably didn’t deserve to be feats in the first place. Just make sure to change other feats’ requirements accordingly.
Touch = Melee range for all intents and porpoises. It does not tell you about what the power's attack roll/saving throw/action is.
The text of the Lay On Hands ability states:
As an action, you can touch a creature and draw
power from the pool to restore a number of hit points
to that creature, up to the maximum amount remaining
in your pool.
From Range (Players Basic p79)
The target of a spell must be within the spell’s range.
For a spell like magic missile, the target is a creature.
For a spell like fireball, the target is the point in space
where the ball of fire erupts.
Most spells have ranges expressed in feet. Some
spells can target only a creature (including you) that you
touch. Other spells, such as the shield spell, affect only
you. These spells have a range of self.
Basically, if you are adjacent (on a square grid this is in an adjacent square, in a gridless style, this is 5' or less away (or in melee range without reach if that's what you're tracking).
Lay on Hands doesn't require an attack roll, it just happens. There is not a specifier that the creature is willing, again, if you can touch them it happens. Your DM may want to include a saving throw or make it a melee attack, but this is would be a house rule, not a RAW interpretation. The RAW here is that if you're in range, and there are no qualifiers, the effect happens. If you want to add a house rule, take a look at the Light cantrip for a solid implementation.
Also, it's worth asking yourself why you want to use it on an enemy? It has no negative effect on them, and would mean you are restoring them HP.
You can knock a creature out with a melee attack
Note that this only works with melee attacks. So ranged attacks will still kill. Though it is good to note that melee spell attacks do still count under the rule (see another of my answers for a bit more discussion here).
This is the only rule that provides a mechanic for knocking out an opponent with an attack instead of doing lethal damage.