Keep them, but keep them rare. I like that there are a few flavorful but odd rules in the game. I've written
before about how this is actually the kind of thing I love in 1E even if it's not the smoothest rules-wise.
Odd rules are troublesome if they show up all the time or would lead to a dramatically wrong way of playing, or make a deck fail to work as plannned or even illegal. The old Q-Flash is a perfect example of "bad rules weirdness", a lot of players had no idea what to do with Q-Events and Q-Interrupts without having access to the QC rules supplement. Some people stocked Gift of the Tormentor in their own draw decks, etc.
By contrast, what happens if somebody plays dual personnel without knowing all the rules intricacies? If they just treat them as a regular personnel card without any special rules, 95% of the time you're doing the right thing anyway, and in the rest of the cases you're usually close enough that the game still goes smoothly. This is actually the good kind of rules weirdness, where things "fail gracefully." You can play the game perfectly fine without knowing it, and it's a fun little nuance to come across when you do.
I do think that there are too many dual-personnel. They should be rare, and representing cases where the two people are very closely linked over a long period of time, not just "they served together on a mission" or "they both appeared in the same episode." Here is my classification of dual-personnel... I think this is all but I may have missed some
Definitely yes -- there is a strong story reason why the cards are together and have to stay together
10 and 01
Ah-Kel and Ro-Kel
George and Gracie
Jean-Luc and Beverly (arguably the strongest of them all, in the episode they could not be physically separated)
Maybe -- they were working closely together, in physical proximity, over many episodes and/or inseparable friends
Anjohl and Winn
Culluh and Seska (although a lot of their collaboration was remote)
Jake and Nog
Rebi and Azan
Sisters of Duras
The Twin Mistresses of Evil (iffy, but they were referred to as a pair more than separately)
The Trois (but in the icky sense of them pressed into Ferengi servitude together, in
mode definitely not)
No -- just friends or romantic partners, or serving on a mission together, no strong reason they HAVE to be physically together as an "item"
Sergey and Helena
Beverly and Will
Data and Picard
Data and Geordi
Mr. and Mrs. Troi
Sons of Mogh (but maybe "promoted" as counterpoint to Sisters of Duras during "Redemption")
The Foragers (but I might bump them up to "maybe" since it's probably not worth making 2 cards)
Third and Fourth
Worf and Jadzia (the episode "Change of Heart" may be justification for bumping them up... on the other hand, the consequence of that episode is that they were never on a mission together again, which in gameplay terms would mean they should have nemesis icons!)