Yes and no. Yes, shouts are basically spells available to everyone, which cheapens magic. No, they're not the reason for Skyrim's weak magic system.
Spellcrafting is gone. Conjuration is a shadow of its former self. Mysticism and alteration disappeared almost entirely. This is the real problem, not shouts.
Having a seperate button for casting spells is ridiculous, if I'm carrying a sword and shield, or a two-handed sword, how exactly am I casting that spell? Shooting it out of my eyes or nose or something?
Is it more unrealistic than shooting it out of your hands? I don't know what TES lore says about it, but as I see it, it's perfectly possible to cast a spell by simply saying its formula. Or even just think it - will it - and it's done. You don't need to wave your hands around.
Just playing devil's advocate. I agree that putting spells in your character's hands was an excellent decision. It makes us choose what we want to focus on and let's not forget it looks great! One thing that Skyrim did really well is spell visuals, it's a pleasure to watch my mage burn his opponents to a crisp.