Actually it can exist. During the conversation Mab says to Maeve that she has not been doing her duty. So we know that the world won't come to a crashing halt if the Winter Lady stops fulfilling her duty because Maeve wasn't doing the duties of the winter lady.
And Rashid actually said that a handover of power most years wouldn't be a problem at all but with the increase in the outsider's aggression and Maeve's attitude it would be a huge problem. Not that it was impossible.
And of course it seems to me that most of the duties of the Queens is done pretty much automatically by the mantle. IE the huge war that was going on without Mab needing to oversee it personally every second. No reason to believe that everything would fall apart the second somebody inexperienced gained the mantle. After all Mab at some point gained the mantle without the universe crumbling.
Do you realize how much shit started falling apart just by *Lily* getting the Summer lady mantle? Did you even read into all of that nonsense? Lily was inexperienced and lonely (and stupid)enough to be swayed by the first member of the court to show even a hint of niceness to her. Titania was completely wrapped up in her grief and Maeve was able to twitch Lily around like a puppet. And Summer is only there to keep Winter from doing dumbass shit to mortals. For fuck's sake, if the wrong person got the mantle of WINTER LADY, who at least has some responsibility to PROTECT EXISTENCE FROM THE OUTSIDERS, it would be REALLY BAD. Maeve was influenced by the Outsiders and was fucking things up left and right on purpose, and we probably have yet to see all the shit that Mab was not able to cover for. Molly at least has a grounding in the way the Fairy Courts work, she has the right magical strengths to be able to understand her power, and will most likely be able to have a reasonable enough grasp to figure out WTF is going on before end game. Tempus Fugit as Nicodemus likes to say.
Also keep in mind that the Fairy mantles do weird ass shit to you. Harry can only barely keep the mantle of the Knight in check and he has years of mental training. Bob said as much as well. You can see at the end of the book that Lily gets so absorbed in the emotional nature of the Summer Mantle, and that she has a ridiculously hard time keeping it in check, and she nearly kills Fix because of it.
Mab is already doing a shit load to cover up Maeve's lack of working. This is evident by the way that she blatantly ignored the Red Court trespassing in her territory. It was clearly Maeve massing troops on Summer's border to keep them busy while Mab was distracted with something, most likely Outsiders or Denarians acting in concert with them to attack Arctis Tor. (Which is also likely around the time Mab starting realizing that Maeve was messed up)
Rashid was specifically referring to Maeve ascending to Winter Queen, when she is insane and erratic. And just because Rashid only referred to it as a "huge problem" does not mean he isn't understating the issue.
Mab most likely gained the mantle at a time that Winter was not in the middle of the one of biggest push on the gates in recent history as well.