Why would the Soviet's independently develop a highly flawed project? This article does a decent job answering that: http://www.popularmechanics.com/space/rockets/a9763/did-the-...
Probably a few reasons:
* At the point of starting Shuttle operations, the flaws of the design weren't as apparent, especially not to general public.
* Even though it LOOKS similar, it's actually not all that similar in design. The main difference is that it doesn't actually carry engines (which are the most expensive and problematic part of Shuttle due to their planned reuse) - Buran was taken into orbit by an expendable Energia rocket, which "solved" the problems with expensive engine rebuilds and testing.
* At the end of the day, Buran never got past the prototype stage. It flew a single mission (empty, fully automated), landed and was then shelved. Only two prototypes were ever built.
A shuttle actually works fairly well at around 1/5 the size. Lower thermal stress means no tiles. It would have a single ideally swappable engine large on board fuel and no external fuel tank. Still needs SRB's but those actually work fairly well.
I think they did do satellite maintenance from the shuttle a few times, most notably on the Hubble telescope.
The Airforce also helped drive the payload (weight and dimension) requirements, but I feel that this is secondary to the cross-range requirement.
As I'm sure you know, the USA actually has an operational tiny "shuttle". But for others here, I wanted to link to it, because it's cute. It looks just like a baby shuttle.
I put the word "shuttle" in quotes, because it's actually not a shuttle, but an unmanned reusable orbital spy spaceplane. Or is it?
https://en.wikipedia.org/wiki/Boeing_X-37
http://phys.org/news/2016-05-super-secret-x-37b-space-plane-...
It's rammed with fantastic photos by Ralph Mirebs of the hangers at the Baikonur Cosmodrome used to house it (complete with an ageing, abandoned Buran inside).