Not really.
It is within the player's control the degree to which they have reach. If you give reach weapons the ability to do OAs at reach, you make reach weapon the only kind of weapon worth having (since they got rid of the 'can't attack at close range with a reach weapon' rule). Especially for fighters who could then stop their opponent 1 square away and attack with impunity if they lacked reach.
As a result, all or nearly all characters (and certainly all melee classes) will arm themselves with reach weapons and have reach all the time - thus making your statement false.
And that is the point.
In 3.x, it made sense for reach weapons to have reach Attacks of Opportunity because benefit was balanced (except in rare cases) by the inability to attack close targets. You were choosing between attacking reach targets with regular and AoO or attacking close targets with regular and AoOs.
In 4E you have the full ability to attack adjacent targets with both regular and OAs AND you have the ability to attack reach targets with regular attacks. Adding in the ability to attack reach targets with OAs is thus overpowering (relative to non-reach weapons).