Don't think of veins as solid pipes. Veins are floppy, dynamic. So when there's something "stuck" in it, it tends to stay still by virtue of the elasticity of the wall around it (I think of it like a brick in a sock). It irritates the walls of the vein, inducing inflammatory responses around the clot (which is why you can get pain and erythema arounda DVT). The coagulation and anti-coagulation cascades are dynamic processes, and blood continues to flow around the clot. Think of a glacier in the ocean. There's water flowing around it, eroding away. Heat melts the glacier, frost solidifies it. Occasionally chunks of the glacier can break off and travel away in the water. This is why DVTs can "grow" up into the iliacs and vena cava. It's why chunks can break off and throw a PE.
Part of the reason DVT prophylaxis is such a big deal is political ("never events" and the like). But part of it is that PE can be such a sudden, irreversibly deadly event. I've seen a patient die of a PE in-house... they have that look of "impending doom", eyes wide, gasping for air. It's something you'll never forget.
Don't know of the correct answer in regards your to question about surgically removing it, but my suspicion is that it's been studied and its a risk/reward issue. By disturbing the clot, you risk throwing an embolus downstream, most clots form in the DEEP veins (by virtue of the name) so it's not an easily accessible site, post-op complications, etc.