Sure, and while we're at it, why not just let wizards turn undead, too...I mean, seriously, the whole thought process behind classes is that nobody does everythig, and very few people should be able to do a couple of the things...if you want an arcane spellcaster who can cast healing spells, go with a bard...if you want and arcane spellcaster who can gain all the possible benefits of arcane spellcasting (specialization, summon familiar, bonus feats, etc) and be able to cast healing spells, then multi-class...but creating a character who can be a 20th level wizard with (major) healing abilities is just silly...i mean, why not just buy a jug of endless healing potions? or that sumoning creatures with healing abilities trick works well, too...hell, when it comes right down to it, start your arcane spellcaster as a rogue and use all his initial skill points in User Magic Device so that he can use healing wands or clerical staves or rods...there are so many simpe solutions to your dilemma that it seems a travesty to wiggle your way past the intent of the division.
What I always say when a player suggests a new rule for his/her character:
If you can do it, so can the NPC's; is that what you really want?