Imagine Bibarel with Double Team, oh the horror...
DT in Baton Pass chains would be many magnitudes more horrifying.
Sleep clause is 100% necessary, else people will just whore sleep or the fistful of pokemon that are immune to sleep/use STalk efficiently.
Freeze clause is not very necessary since freeze almost always means death for the one pokemon and it's a fairly rare occurance to boot.
Species clause is not very necessary for the reasons given above: you'll either double your advantage or double your disadvantage. Also, not very many pokemon are worth doubling up on, mostly just mixers and they are counterable in the current system.
OHKO clause is marginally necessary to further reduce the odds of the opponent getting a "free win" from (3/10)^6 to less (ideally zero). There are quite a few good pokemon that can abuse OHKO as well, Resttalk Lapras with Sheer Cold and Horn Drill comes to mind. Articuno would get some work as a phazer with Mind Reader for sure and I'm sure Rapidash wouldn't mind some Choice Scarf Horn Drill either. Or how about Stallrein with Sheer Cold? Scary.
The argument can be made that "using an inaccurate OHKO move over another move in that slot is justification for allowing it", but most people will agree that a 30% chance at OHKOing all pokemon is always better than the common case: a 100% chance at never KOing your counter or 3+HKOing something neutral.
DT clause is marginally necessary since people try to avoid clawing their eyes out. Going back to the previous example and assuming that you have a pokemon with 6 DTs (or evasion stage equivalents) and the ability to 3HKO the entire opposing team, trying to reduce the odds of a "free win" from (1/3)^18 to less is ideal. The more common situation would just be an annoying wall that becomes magnitudes more annoying when you have to hit it twice in a row to stop it's ability to heal off all damage.
Item clause is not needed at all, it's a directionless restriction carried over from the main game. There's nothing inherently wrong with 6 leftovers, only that Pokemon says it's bad.