The main points, Bocate has already dished out. Headless basses in particular have this notion or reputation that they always seem to come with that paddle body, that was on them when they where around first. You must - just as Kubicki has - a full body.
I like headless instruments. Both on guitar and bass. But not because they're headless. They're immensly more practical in all senses. I remember when - say - Floyd Rose locking tremolo system came around. I started to wonder what the headstock would be of any use then. ABSOLUTELY NONE! So when headless came around, especially with double ball end strings I thought "This is MY locking system". The strings locks where they end. No reason to have angle behind nut or zero fret, no nothing. And on top of this. On my headless guitar I change ALL STRINGS AND TUNE THEM UP AND THEY STAY IN TUNE WITHIN 5 MINUTES. That's before anyone with a Floyd Rose Tremolo has got rid of all residue from a broken e-string yet. It takes AGES to tune and change one string on a guitar with FR on. Speaking of reaching the tuner, I play the open strings with left hand, just grabbing them WHILE my right hand is on the tuner back at the bridge. Just snap and play a pull off with the left hand, and then tune up. The thing is, that ON BASS this is a way more convenient method if you have to tune WHILE playing. No reach over with you right hand over to the headstock. But a catch 22, since headless and double ball end strings always stays in tune when you've tuned them up in the first place, and very rarely drift, this practical advantage is sort of ... futile.

On bass, 4 string, I am down changing strings (all 4) within 3 minutes 40 secs. And even then, tune them up, and they STAY in tune. No excess slack or lenght of strings behind the nut.
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Now, they do wiggle, and bounce around - just as was said before - when playing intensely. You have to use the thumb at the back of the neck as a stabilizer from then neck moving in and out. A Headstock can provide a counter pivot for such things. There's very little movement pressure that has to be used in order to knock the neck out of position when playing(fingering), leaving that you miss some frets or notes. Some people doesn't believe this. If you have a rigid strap and a ergonomic built body you could remedy this somewhat. I have trouble today playing basses with headstocks on, rather than the other way around. Also keep in mind that an instrument does not have to be as lighweight as possible. If it's well made and well balanced, it can be quite heavy without anyone really noticing it. But all in all, remember, there are just as many variations on good and bad basses with headless as with headed ones. Just because they are headless doesn't automatically mean they're something better or worse. Just as with headed ones. And I for one doesn't go by the looks that it looks wrong or broken. I have seen more basses with broken headstocks, and .. well.. you get it. Remember what flak Fender had to take when elelctric basses or guitars came around in the first place, at the beginning of 50s. They looked wrong too, and then some. Conclusion: whether a bass has headstock or is headless is not a deal maker or breaker for me. I'm good with either of them really. You can make balanced basses with headstock today. No that much of a rocket science.