FET DC operation in the ohmic region if the SOA curve doesn't have a DC line?
When using a FET as a switch it makes sense to choose a FET, that is designed for switchig. These (MOS)FETs typically include a parameter called RDS(on) in their parameter list. This is the remaining DC resistance, when the FET is switched through.
Typically, a FETs DC capability is limited in the following ways:

Maximum Drain current.
Maximum power dissipation or junction temperature.
Maximum breakdown voltages on Drain and Gate pins.

As long as you don't overload any of these parameters, it is, generally speaking, fine.
FETs for amplification (operation in saturation) are a little different by design. For an amplifier FET it is usually not that important to have a low RDS(on). Instead parameters like the Drain-Source parasitic conductance, noise, linearity, parasitic capacitances etc. are optimized. These devices are just not made to be operated in the linear region and can perform worse than a &quot;digital&quot; switching FET.
However, as long as you don't overload the FET with regards to the above constraints, it will work. But again: DC performance can be a lot worse than a FET that is made for switching.