Who grounds drains? In SMPS for example, the drain (e.g. mains referenced) normally has to be isolated from the heatsink (e.g. ground referenced), going to some lengths to ensure this is the case -- at expense to thermal performance and EMI response! (Or the heatsink gets mains referenced, then itself must be isolated from everything else.)
So it's quite convenient that they've done that, and indeed pretty much mandatory to obtain the performance that LDMOS is capable of (maybe not GHz in that package, but 100s MHz, easily enough).
Note, it does assume common-source connection, which is the most common topology, due to best power gain and efficiency, with a reasonable compromise to frequency response / isolation / stability.
There have been common-gate or common-base devices, I think more in the past and not so common anymore now that feedback capacitances have been optimized so well?
Have also seen some common-collector devices, like, I have an old amplifier module that is supposedly of this type, with integrated transformers providing step-up at the input (the base voltage obviously needs to be pretty high, there's no voltage gain in an emitter follower) and matching at the output. But yeah, because of the poor voltage gain, these tend to be uncommon.
Or I suppose you could use isolated base/gate drive, given a transformer with good enough isolation that the feedback capacitance doesn't screw everything up -- then its response is common-source as usual, but noninverting (give or take transformer phase).
Anyway, as for biasing, sure, you can do a servo or something.
Usual way is open loop, usually something like a resistor voltage divider to give fixed gate voltage, with some diodes stacked into the bottom resistor of the divider to give it a bit of a tempco. YMMV how many diodes and what ratio to use.
If you want better stability or tracking than that, a servo can monitor supply current -- mind, strictly for class A operation, because otherwise, well, y'know -- and yeah, sensing supply current is probably the better way as you don't want to un-ground the source. (You could, putting a shunt resistor there, and stitching around the island thus created, with bypass caps to keep it well grounded. But, that's a bigger PITA I'd say.) Current sense (probably a shunt resistor plus a current sense amp), error amp with nice slow compensation, gate bias. Do set some limits on the error amp's output range: no sense in being able to give it like +15V if it should only need 7 or 8 in the worst case condition!
And yes, the bias circuit can be powered from drain supply, or you can use a lower supply if available, to save on power dissipation. Not like the gate needs any current, a few mA should be more than enough even with old opamps.
Tim