lorna, I hear your point, but possibly you've never really liked/fancied anyone on dating sites, not as much as OP liked the guy. Unlike you, she said she didn't fancy ANY men from online before that she met them, yet she was hugely attracted to this one. In this case it's really hard to forget it and to switch quickly to others. Some people are extremely selective/fussy - it's not superior or inferior, it's just what they are.
Others are quite easily attracted to people - as you are - but then can quickly cool off to if these men are disappointing. But not everyone is like that. I was just saying to OP, they are not on the same page with this guy, she wants to find one guy, and he wants to try all the sweets in the shop - it's not wrong of him per se, but it's the wrong man for her!
Of course she does need to move on, as I suspect she's now annnoyed with his gameplaying - rightly so! I still claim, OP, that he DOES want an invite from you to come to your place for sex, that's the explanation why he keeps puttong ball in your court. He won't offer just a date as he's not interested in slow dating - if he wanted this, he would have done!!