There is no mental disadvantage to alternating, the only people who think that way are people who don't alternate. A rough start is natural, as it is with everything you're a novice at. Like you didn't suck when you started playing osu regardless of play style, this is just a new way to play, of course it would be difficult at first for most people. I alternate perfectly and I play HR most of the time, my accuracy and aim are my best traits.
Now, do you really think I'm capable of aiming every small circle on screen and tapping on time to get 99% OD10 accuracy while also "straining" myself to always use the next finger I'm supposed to use, alternating perfectly? I'm not that good.
This applies to all play styles, like people who alternate pen tap + keyboard key (Black Sheep style), sure I can't do it, but they can and they have no issue whatsoever handling tricky rhythm patterns and bpm changes, because it's their play style and they're used to it.
tl;dr I don't have to think, notes appear on screen and my body moves on its own. Also I used to single tap, my play style gradually shifted to alternating over time somehow.