...I'll tell you all the truth: this is exactly the reason why I have a bit of a lethargic attitude towards going up mountains like Matterhorn, Mont Blanc, Grossglockner, Gran Paradiso (for all four of which I would need to hire a mountain guide anyway!) and the like...On the good days, one has more the feeling of being on a motorway during rush hour rather than being one with a great mountain!
You're absolutely right and I think it's safe to say you're not the only one that feels that way. I've struggled with this as well and tried to find ways to avoid the crowds like going mid-week, off season or even off route! It's tough in a highly populated region like this, but I still think it's worth the pain for what you gain. If you do get motivated to head up the big hills, I wish you all the best!