At this point instead of asking yourself why he doesn't want to marry you, you should probably be asking yourself why you are still hanging around waiting for a proposal. Even if he does it now, isn't it tainted?
So if you had two choices:
a) stay with your partner, but knowing that you will never ever become his wife, or;
b) you want to be a wife more than you want to be with this man,
which would you choose?
So as an experiment - think about those two options without thinking about houses or finances or anything like that - just with your heart - what would you choose?
Based on your answer, then you need to decide if you are staying and never being a wife, or leaving to find someone who does want a wife.
If your choice is to stay, then tell him to shove his proposal up his traditional arse -and mean it! But that you DO want whatever legal paperwork drawn up to ensure that you have legal protections of your assets, and your children will have your surname added to their names.
Meanwhile, since you are financially vulnerable and he's not followed through on his promises, you are returning to your career and that you with both split each and every household and child-related cost proportionally based on a % of your salary.
You need to protect yourself. Right now he could just break up with you and you get nothing except the barest he can get away with paying for the children, and half the cost of your house less the massive deposit he paid that he ringfenced.