The obvious reason to exclude healing spells from the Wizard's list is, of course:
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And, really, that's all the reason 5e needs to (not) do anything...
... in the PH.
In something as peripheral as UA? Not so much, as long as something is opt-in optional, tradtionalists can just not opt in (and look down upon, mock and deride anyone who does).
But, there is a game-play-dynamics reason, too. The Wizard, more than any other class, /is/ his spells, the spells he knows define him (and he can know more and more varied & situationally-useful spells than his close relatives, the Sorcerer & Warlock), the spells he actually casts are his primary contribution to the success of the party. Healing spells are critically important in 5e, so slots can be used for them, they often will be. When a Cleric uses his slots to heal instead of cast something more spotlight-grabbing, he still has channel divinity and he's still a bit tougher and able to contribute in combat than the Wizard. When the Druid blows his slots on healing, he can still shapechange. Similarly, the Valor Bard run out of slots by healing needs still fights, and the Lore Bard is still a skill monkey.
So 'letting' a Wizard heal wouldn't be doing him any favors.