I think this is why the Alcubierre drive will become critical even at well below light speed. Assuming I understand the physics correctly, the bubble of space around the ship is not moving (very fast) relative to the ship and so moving at fractional c will see an increase in flux but not the blue shift. You’re still hitting every spec of dust in your path, but not turn the entire cone of the universe in front of you into gamma rays.
At some point the warp drive might be cheaper than the shielding.
If an alcubierre drive can be created,even inside the bubble of normal space time you would probably die. This is because of the Unrue radiation that is created by compressing the space time in front of you. Also, it seems that even with the best theoretical approach you still need the mass equivalent of Jupiter in exotic matter to make it work for a small ship :/ Spacetime is extremely resistant to compression/expansion.
At some point the warp drive might be cheaper than the shielding.