I don't know if it's just me but I've noticed that a lot of people seem to forget just how complex Liam's character is. They forget just how he developed his switch energy. Ever since he was a little kid he's had to play as someone else, because he had to. By the time he's in NYC with Sherlock, the only things he knows about himself is that he likes math, he wants to be with Sherlock and he still wants to help people. That is William's core is that he wants to do good and he's learning that he can do good by doing good. He didn't like to be the Lord of Crime but if he didn't become that version then nothing would change, that's what he thought. So up until current time he's just been doing what he needed to so he could survive. Which is where that “dominating” or “switch” energy comes in. I'm not saying he wouldn't like to but he's doing it because the person he was helped him survive. During his time in NYC he's literally trying to figure out who HE is, who is WILLIAM JAMES MORIARTY. He's more vulnerable(earning the nickname crybaby William), he's starting back at square one, and he's in a completely different place. Sherlock is quite literally his place of comfort, NYC gives him a chance to be away from everything and not have to be in that survival mode. It's like when someone grew up in a household where they had to recognize everyone's footsteps and then when they are finally safe from that place they still have that habit of knowing footsteps, Liam is learning how to be his own person rather than his Lord Of Crime persona (or pretend he is OG William that society thinks he is). So I don't think at first he would be very dominant or switch with Sherlock, and Sherlock wouldn't push that. It wouldn't be until he asks Sherlock to let him continue to live with him and be by his side that he would develop that switch energy because at that point he knows something/someone he wants.
In line with this thought, the same could be said about his secondary gender(omegaverse). A lot of people think he could be an Alpha or an Omega with Sherlock but to me it's deeper than that. Because he had to be the way he was to survive, he would've been an Omega presenting as an Alpha. Because of the time they're in, being an Omega male(rare) was shameful. Due to this William had to hide the fact he was an Omega. This also aligns with his personality. Of course Sherlock first meeting William knows he's not an Alpha but doesn't say anything(nor care). When they live together in NYC William doesn't have suppressants or blockers and experiences his first heat without his medicine. Because of having to use blockers and suppressants his heat hits hard. Sherlock helps him(and almost dies lol)