Asking the father is spoken about a lot where I come from though I only know a couple men who did so for certain, all of the older generations (though I left at 17 so don't really know much about mine). I don't know anyone having been turned away though all blessings I have heard of involved agreements being made as part it being granted (men working for their bride-to-be's father, housing arrangements, having qualification and even degree fees paid for and similar) which I can see makes sense as something I could see being agreed with between the couple as the best way to go even if I would never do so myself.
This was the situation with a man who asked my grandfather to marry my aunt, him and my aunt agreed that was for the best. She asked my mother for advice on that which is how I found out about all of it when I was 12 or so. They lived with my grandparents for several years and my grandfather helped pave the way for my uncle's career, my grandparents provided childcare and lived with them in retirement. Even then, the bride-to-be is still asked first though and if the groom-to-be discusses it and asks a blessing from the father, it's done with her there so the idea of asking the father or talking with the family without both parts of the couple present isn't part of our traditions which, as is probably obvious, has pretty old patriarchal transactional roots. Those who don't want to enter that type of arrangement generally don't ask for blessings, it's seen as sensible to do so - why make life harder if you don't need to, but those who stay in the community without doing so like my sister or whose father's don't give a blessing aren't at any other disadvantages, if that makes sense. It usually just means there is no or no longer any relationship between father and daughter, but the wider community doesn't really care as long as people play nice about it (not making scenes about family issues is seen as far more important than getting a blessing to marry).
To me, someone who asked my parents would be like someone who proposed with a diamond ring - they obviously don't know me well enough to be asking me to marry them. I wasn't 'given away' when I married and I walked into the registry office with my now-spouse at my side. Neither of my parents were involved. I'd rather celebrate with my children after they make the choice than be that involved in who they choose to legally bind themselves to. If they're old enough to do that, having anyone asking me or their father is just asking for them to get some sort of herculean tasks for our amusement.