With all due respect to Elon (and he is due a lot of respect!)...

The physical plant for F9 launch (sub-chilled kerosone and LOX, 200,000 gallons water for the flameduct, the strongback, the concrete mountain of the pad) is much more involved than the physical plant required for landing (basically a thruster-stabilized barge). The required launch infrastructure just would not fit on a droneship.

Also, the droneship absorbs the energy of an empty booster traveling at 10s of meters per second, and possibley the partial thrust of one Merlin rocket engine operating at 40% nominal thrust.

A full-up F9 stack (booster/2nd stage/payload) weighs about 1,210,456 lbs. A launch with nine Merlins at full thrust would have 22.5 times the thrust of the droneship landing, say 1.7 million lbf of thrust. I expect that would be enough weight and thrust to make the droneship wobble a bit, and the rocket exhaust plume would probably toast everything on the droneship.

Apropos of nothing... I've come up with a screwy idea or two since I've been commenting on the SpaceX reddit. I don't feel so bad when I see some of the comments that are documented on https://www.reddit.com/r/ShittySpaceXIdeas/ .

One guy suggested using a decommissioned super-size, nuclear-powered Nimitz class aircraft carrier as a launch and landing platform! Ignoring all engineering issues, could you imagine the daily cost to keep that rig afloat? The catastrophe if an errant launch or landing compromised the integrity of the nuclear plant. The mind reels...