The Temptation to Cookie-Cutter

"I’ve been to McDonald’s in Russia and it tastes exactly like in the US. Is there a way to avoid this homogenization with large growth?"

That's exactly the magic of McDonald's. Having a different experience at every restaurant would be bad from both a customer perspective and a management perspective. Customers know exactly what they will get every time they go to a McDonalds. Franchisee's have clear processes and procedures to follow for food preparation, hiring, etc. There is no ambiguity and very little variation (I'm glossing over the fact that there are some very large and necessary differences due to localization issues).

I think in the examples given, hiring can be a huge differentiator (Starbucks, Applebee's, etc.). A friendly/knowledgable barista, or a skilled server can really humanize the purchasing/eating experience and perhaps mask a lot of the chain-store feel.

I think a lot of people actively seek that consistency, especially while traveling. Knowing that a McDonalds is a McDonalds wherever you are provides a safe choice for a traveler (especially since they're everywhere). That's what a chain provides, consistency across locations, not a unique experience.