If fact you can do this as a house rule with existing 4E. It doesn't make you more 'powerful', it just gives you more options.
More options = more versatile = more powerful.
BTW I hate having to swap out powers as you go up in level (I forgot how to swing really hard) and using the same at-wills over and over again.
Yeah, I'm not too keen on that myself.
Edit: You'd think WOTC would love your character being able to collect powers, especially in the form of cards, MTG and all that.
Oh and the ability to scale up powers so that a 1st level power can be boosted up, say, to a level 6 version.
How about the following?
Since the vast majority of powers do damage, let's start with a model of two types of powers: damaging powers and utility powers. The PC gets x number of each (for now, we don't care what x means and it could be a different number for each).
For the damaging powers, let's start with a model of:
Weapon melee basic attack
Weapon ranged basic attack
Mystic melee basic attack
Mystic ranged basic attack
Mystic at this point could mean anything with is not using a weapon. Force bolts from a wizard, divine power from a cleric, whatever.
All PCs at first level have the ability to use one or more of these four types of basic attacks.
At will powers then become modifiers to these attacks.
For example, a power that pushes a foe one square. The entire power takes a single sentence (or two depending) on a character sheet.
Instead of this vast plethora of cards, or pages and pages on a character sheet, we instead have for a first level PC with 18 Str and a Longsword:
Melee Basic Attack Basic Attack At-Will ✦ Martial, Weapon
Standard Action Melee weapon
Target: One creature
Attack: +7 vs. AC
Hit: 1d8+4 damage.
Special: You can use an unarmed attack as a weapon to make a melee basic attack.
Cleave
You hit one enemy, then cleave into another.
Hit: Melee basic and an enemy adjacent to you other than the target takes damage equal to your Strength modifier.
Crushing Surge, Invigorating
The feel of your weapon crunching against the enemy puts your heart back in the fight.
Hit: Melee basic
Footwork Lure
You press the attack, engaging your enemy before falling back and drawing him after you.
Hit: Melee basic and you can shift 1 square and slide the target 1 square into the space you left.
The entire At Will damage portion of the game becomes a serious of minor special effects that get added to the core basic attack.
Encounter damaging powers could then take the form of:
Melee Advanced Attack Advanced Attack Encounter ✦ Martial, Weapon
Standard Action Melee weapon
Target: One creature
Attack: +7 vs. AC
Hit: 2d8+4 damage.
Covering Attack
You launch a ferocious attack at your enemy, allowing one of your allies to safely retreat from it.
Hit: Melee advanced and an ally of yours adjacent to the target can shift up to 2 squares as a free action.
This would need to be controlled in some way as to how many Encounter powers the PC could use, but having the PC gain more options would be doable.
In order to acquire the additional basic and advanced attack options, the PC would spend a feat something like "you gain 3 mystic basic attacks, either melee or ranged, of your choice". This ensures game balance between the PC that has a lot of different basic or advanced attacks (i.e. many options at all times), and the PC that has few, but used his feats for other things.
I do think that a PC should not be able to acquire every power for that class in the game without spending resources like feats to do so.