If the US had the space shuttle, the Soyuz, and common sense, they would also drop the space shuttle and fly the Soyuz. But apparently the US had neither the Soyuz nor common sense.

The Buran only existed in order to send a message. And it was also technically better designed than the space shuttle.

Sure it seemed more capable, but it was also designed for propaganda. For example the version of Buran that actually flew sacrificed the spacecrafts engines to get more stuff into orbit. The shuttle on the other hand returned with them. If you want a space truck, the Buran failed a primary design goal.

Now NASA did end up spending a lot of time refurbishing those engines, but if they wanted more frequent launches they could have simply built more engines. The program dramatically misunderstood how much they would be flying resulting in vastly higher costs over time.

Which was the major design flaw of both systems. Dig into things more and Buran was simply an even worse fit for either program than the Shuttle ended up being.