Could(and should) it be done? I could imagine these being a subsitute for those who start out boots+3 potions or those who delay upgrading their boots for later. The stats could be something like this:
+80 health(cuz all Doran's have this)
Enhanced movement 1
UNIQUE passive: 5% cooldown reduction
And maybe: +3% movespeed

I realize that items are very hard to make+balance, so please do not rage or insult me. At the very least, just tell me why they would be bad. Of course, exact numbers can change. I just think there's a niche in the market for these.

Not all Dorans items have 80 health, last I checked...
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+80 Health
Enhanced Movement 1
+7.5 Health regen
+3.75 Mana regen

This will give you the equivalent of 2 health pots and 1 mana pot per minute.

Doran's Shield still has the original health value because there has never been a problem with stacking it. Even if the shield was stacked it is more negligible than the other two Doran's items because it doesn't increase damage at all.

ive actually been considering an item like this for quite a while. however, i think it should look more like this
enhanced movement 1
+ 60 health
+ 5 health regen
unique passive - +15% tenacity.

perhaps a little less on the tenacity but since all dorans items offer buffs based on the main stat of the item, dorans attack matched with lifesteal, rings ap matched with mana regen, etc, this item should get some form of tenecity to match the movement speed. maybe even remove or replace the hp5 with something.

You don't ALWAYS need to replace Doran's Ring/Blade...
Doran's Blade/Ring are still highly cost effective through-out the entire game...
Doran's Ring/Blade lose slot efficiency as the game progresses...

Doran's Boots WILL be replaced in almost every game, because other boots are simply better...
Boots = Cheap stats which you would otherwise be getting regardless...
Boots = MS, which you NEED, because everyone else will have MS...

Doran's Boots will just put you further behind in your build, because they're not much better than Boots of Speed, but they sacrifice a huge amount of potentially cost effective stats...

Either: Buy Boots of Speed... Upgrade them... Gain highly cost efficient stats... Profit...

Or: Buy Doran's Boots... Sell them when everyone else upgrades their Boots of Speed and out-paces you... Lose money... Un-Profit...