When using a fixed derate, the new thrust rating becomes the maximum thrust available. Since you have less thrust, in an engine failure, the yawing moment due to thrust asymmetry is less, therefore you don't need as much rudder authority. This means that your Vmcg/Vmca (minimum control speed) is lowered. In some situations, you have to increase your takeoff speeds due to a high Vmca which means a longer take-off roll. With a fixed derate, your Vmca is lowered so you don't need such a long take-off roll and you can depart with a higher take-off weight.
Now you might be thinking that using assumed temperature, you would also have lower thrust asymmetry in an engine failure. However, the rated thrust is still at 100% and you can press TOGA again to get the rated thrust. Hence, assumed temperature does not give you any benefits in terms of Vmca.
In fact, if you exceeded the fixed derate in a Vmca limited situation by manually advancing the thrust levers, you could potentially end up in a situation where you do not have sufficient rudder authority to counteract the thrust asymmetry.
The other benefit of the fixed derates is that you can use them in any situation. Assumed temperature is not permitted in some situations, such as a contaminated runway (snow, ice, slush, etc.) Assumed temperature is only permitted on dry and wet runways.
In response to the question as to whether fixed derates are "safe": you don't know if any take-off will be safe until you perform your take-off analysis, either manually using charts/tables or with software.
In response to whether derates are "easier" to do than assumed temperature: it is exactly the same process. Even using both derate and assumed temperature together is the same process. Boeing publish a set of charts for each of TO, TO1 and TO2 take-off thrust ratings (in the FPPM; the FCOM only offers a basic set of charts/tables). From these charts, you can either work forwards to find the maximum weight you can safely take-off with, or you can use your actual take-off weight to work backwards to find your assumed temperature. If you ever find that your actual weight is above the limit weight or that the ambient temperature is above the assumed temperature, then it is not safe to take-off.