I don’t deny that giving up something and replacing it with prayer is beneficial. However, I believe to give up something in and of itself is a form of prayer. So in that respect, the pure fact of giving something up would be beneficial.
But, that presupposes that all prayer is beneficial at all times and places. I don’t think that’s true. Consider, in the OT Law there is a form of prayer called “don’t eat pork.”.
At very least, it was a disciplinary way to give people practice at “not” having everything that their neighbors did – eg: a predetermined Lentin practice that went all year around.
But it became something unhealthy at a certain point, for it isn’t brought into the new testament or affirmed – rather, St. Peter was told to break that fast for the sake of the Gentiles, and look also at what St. Paul says in Colossians:
Colos 2:21 Touch not: taste not: handle not.
Colos 2:22 Which all are unto destruction by the very use, according to the precepts and doctrines of men.
Colos 2:23 Which things have
indeed a shew of wisdom in superstition
and humility, and not sparing the body; not in any honour to the filling of the flesh.
Colos 3:1 Therefore if you be risen with Christ,** seek the things that are above**, where Christ is sitting at the right hand of God.
Colos 3:2 Mind the things that are above,*** not the things that are upon the earth***.
The problem with “giving” up as a form of prayer is that it has a limit in its usefulness.
By giving up too much one presents temptation with a doorway; conversely by indulging too much (gluttony) the same is true.
An act of charity or giving of alms is far superior to the prayer of abstaining.
There are two penitential seasons in the year, and a weekly penitential day – the “Friday” that the Lord was crucified on, The advent season where we prepare for the nativity, and the Lenten fast and mortification. But, by observation, I think people preparing for Christmas are far more in the penitential mood of prayer than those “giving up” as a show of strength against temptation.
An anorexic – giving up all fat during Lent would be an extreme example – but it makes the point that for that person, giving up various foods would likely be sinful. There are some things which one can always give up – eg: sin; but others are of little value to God in fulfilling the two commands – Love of God, and Love of neighbor.
I don’t know to what degree this “debate” between you and your fiancee is important to you; but unless she is persecuting you for giving something up that does good for others (eg:the rice bowl, where coffee $ is donated), consider that fasting can quickly become a point of judgment between you two, and not one of prayer. We are called to peace.