Being that XCOM is ostensibly a military organization, I really doubt an elected "leader" would hold any power over anyone of higher rank. Military forces are not democracies, they are tyrannies.
In particular here, rank is bestowed through experience and competence in battle (being on missions and kills). Thus, knowing what you're doing against aliens puts you in charge. Presumably, an XCOM colonel knows way more than a Squaddie "leader."
Sure, that's in battle, you say, but I'm talking about being in the base, outside of battle. It's not that simple. Military discipline applies at all times. Soldiers must be conditioned to obey orders at all times, which means it has to bleed into noncombat situations. If you get into the habit of questioning your superiors normally, you're not going to follow an order to charge a fortified enemy position, or run across an open field immediately. You might ask why me? Why am I bait? Well, if the flanking element needed a distraction right that moment, and you didn't go... good job, they died. Instant and willing obedience to orders is necessary and has to be constantly ingrained, trusting that your superiors are giving you an order for a reason and instantly executing, because sometimes, even a single second can matter in combat.
That said, leaders should need to earn that uncompromising trust from their subordinates.
Anyways, military sociology and psychology is a lengthy topic I won't go further into. I've rambled enough (plus I'm typing on my phone). I think an elected leader is unrealistic and unnecessary.