I just don't see the problem with allowing someone to play a fully fey character (within the bounds of your game's starting refresh) as long as they are aware and willing to take on everything that means. That means deals are binding, cold iron is a no-no, can't lie (outright), etc.

It is quite evident that any and every fey is compelled by their nature, but by that token, every human is as well. Some just have more freedom to act against their nature (higher refresh). It is evident that the wyldfae are free to act as they will because they are less powerful. They don't have the mass of responsibilities and power that the greater fey do, so they can choose. Sure, they can get called to one court or another, but that seems to be more of a draft. In a case where there was Calling going on, it would be difficult to actually play a wyldfae, but you could explain it as "I'm doing what I can for X Court by aiding the rest of the group in solving the problem", being aligned with the Wild Hunt (in which case you'd have to run with them when they went out), or some other plot related device.

If you look at Toot and the Za Brigade's actions in SK, you can see that they are only on the side of Winter because they're allied with Harry. Toot himself couldn't tell whether he'd go to Winter or Summer when he talked about the Calling with Harry earlier in the book. In a later book, Toot even works against Summer and Winter by scouting for the Gruffs and then warning Harry of Mab's approach. Toot and his compatriots choose to work with Harry (because, it's pizza!), but at any point they could have refused to work with him. Sure, he could have cast a spell or used Toot's true name to compel him into working for him, but that'd be breaking one of the laws.