Intimacy, you're hearing hooves and desperately looking for zebras. It's right in front of your face, you just don't want to accept it.
He doesn't want to be with you. That's why he doesn't want to try. He's not interested. He wants to sleep with you, but he does not want a relationship with you. There's nothing to "try" for, for him. He's clear in his position.
You have emotions which have confused this, and you're looking for another explanation, but you need to call this for what it is.
He doesn't want a relationship with you. It'd be easier for you if he'd just outright tell you that, but he won't, because you both know it'll hurt you and he loses access to regular sex if he hurts you.
FWB won't work, because you are emotionally connected, and even if you manage to balance it and not constantly push him into more, you'll be blindly hoping that he changes his mind. He'll meet someone that he does want a relationship and drop you like a hot stone, and that'll hurt like hell.
Knobs don't come with signs. Some knobs look perfectly nice and are well behaved, but they just treat some people like knobs. He is acting like a knob to you. He could be Prince Charming for the rest of the world, but he's asking you to sleep with him and be a stand-in date when he's bored and horny, but not get attached, not expect anything of him, and not mind when he finds someone he does want to actually date.
Not only that, but he's slept with you three times and he didn't want to see you whilst you were on your period. He's not even a good FWB. You just can't see it because you're love-blind.