That won't go down to well with her that she's a 10 out of 10 and her boyfriend won't propose.
Not saying theres anything wrong with not being engaged after 3 years, but for someone like Luke who seems very romantic and loves dropping the cash on other material objects, I would have thought a ring would have been offered by now.
Hes playing the long game because he knows she's not the one. It's as evident as day that he's not as into her as he was when they first got together; He barely puts any effort into his appearance anymore, gives the same presents all the time, doesn't go on holidays with her anymore, won't live with her etc. Sure why would you want to commit to spending the rest of your life with someone who cheats, throws "princess tantrums" (cringe), can't do anything for themselves and is so self absorbed, anyway?
The reason they constantly break up and argue is rooted to the fact he won't propose and this drives her up the wall as she can't comprehend why a man wouldn't want to tie her down as she's so unreal.