I'm also not sure dating your sub-ordinates is a great idea.
This is certainly a point of view with which I'm familiar - I have a friend who just flat out won't do romances because it breaks the immersion for him, but for me it depends on how you define "subordinates."
While it's clear that from a gameplay point of view you're in command in all the DA and ME games, story-wise I'd be hesitant to label all companions as subordinates. There are plenty of times when companions are there because they choose to be, and you have no means of keeping them there other than that your goals align. There are some romance options who I'd definitely class as being a subordinate, some where it's an debatable issue and some who I'd flat out say are not.
Definitely Subordinates:
Ash, Kaidan, Jacob, Kelly, Samantha, Steve
Debatable but still fraternisation within the ranks:
Alistair (technically he's your superior),
Miranda (Again, it's your ship but she ranks higher than you in Cerberus)
Debatable:
Zevran is there because you didn't kill him and he does swear service to you, but he's hardly a warden.
Thane, Jack and Samara, well they are there because the Illusive Man sent you to them, but they aren't really in it for Cerberus's money and they're not a part of Cerberus.
Not Subordinates:
Liara in ME1 is there because you rescue her and because she sees the threat to the galaxy, but she's an advisor and you have no military authority over her, unless you count your SPECTRE status. In ME3 as the Shadow Broker she has a hell of a lot more political clout than you do, and she's there because she chooses to be.
Tali and Garrus are helping Shepard through friendship and the desire to help save the galaxy in the best way they can but have their own positions of power within their respective species' organisations.
Morrigan and Leliana have their own reasons for wanting to help the Warden, but they could just walk away.
All DA2 companions.
Also of note is that depending on how you choose to roleplay Shepard in ME2, you might not accept that (s)he is part of Cerberus at all.
In Inquisition it'll be interesting, as although you're in command, you're really a leader of leaders, so again the question of who is a subordinate is somewhat murky to my mind.