While you can do that, you can also just take a thicker piece of steel as it's typically one of the cheapest materials you can get. Energy spectrum is typically not that hard as neutrons are usually moderated (if it's not fast-neutron reactor).
But embrittlement in pressure vessel is not a major concern during reactor design. Neutron economy is the most important as it has direct impact on nuclear reactor economy. Every neutron = $ (you can ether trade it for fuel regeneration or lower fuel enrichment = lower costs).
In the nuclear reactor design it is preferred to use as much neutrons as possible, and hence try to reflect neutrons back to the core rather than dump them into the pressure vessel. Without reflector you will have very high non-uniformity of neutron flux in the volume of the core and it will be hard to operate.
In VVER PWR reactors reflector is made from water-steel sandwich.
In graphite-based reactors reflector is also made from graphite.
You can see reactor composition example here: https://www.researchgate.net/figure/Horizontal-Top-and-vertical-Bottom-cross-section-of-3D-60-0-symmetric-two-energy_fig8_309576283