One shoulld only fast on Sunday as a preparation to receive the Body of Our Lord, Jesus Christ. Apart from that preparatory fast, Sunday is a day to celebrate the Resurrection of Our Lord and His victory over death and sin and His presence among us.

It would not be good to fast on Sunday. I would be like going to a wedding feast and refusing to eat the food presented to you - your hosts would regard that as a great insult.

Luke 5:34-35
To whom he said: Can you make the children of the bridegroom fast, whilst the bridegroom is with them?  But the days will come, when the bridegroom shall be taken away from them, then shall they fast in those days.

They do in the Eastern rites when the fast is stricter. During Lent, mostly.

Just one more strike against them. It just shows what happens  when priests separate from the authority of the pope, they totally lose God's Sanctifying Grace. Same happened to the original Catholic bishops and priest who started Protestantism.

Notice that in our times, it is the conciliar church that shows this sign of the loss of God's Sanctifying Grace, by their every deed.

I know that it is never ordered to fast on any Sunday, not even during Lent, but if one wanted to, would it be good or would it be a bad thing?

A bad thing.

You have 6 days during the week during which you can fast all you want.

It isn't consonant with the mind of the Church to fast on Sundays. Sunday is the Lord's Day, when we celebrate the Resurrection.

I don't think the saints fasted on Sunday.

Just look to our Holy Mother the Church for advice on this matter -- she has periods of penance, fast days, ember days, but also FEAST DAYS where we are told to rejoice and be happy, to better honor Our Lord, Our Lady, one of the saints, or one of the mysteries of our Holy Faith.

You do realize, of course, that "doing what the others do" and "following the crowd" is virtuous and ideal, as long as those "others" are devout Catholics living a Catholic lifestyle. Being singular even among devout Catholics is a fault, not a virtue. It's a temptation rooted in pride.

There is a time to rejoice, a time to weep. A time to feast, a time to fast.

It's in Ecclesiastes -- inspired by the Holy Ghost. "The Byrds" even took those words and turned them into a song.

One last thing -- when it comes to fasting, you should always consult with your spiritual director. There is always a danger of vainglory, pride, etc. entering in to it. But never would the danger be higher than when you are tempted to fast on Sunday. Imagine what you would think of other Catholics who don't fast on Sunday... You'd be pretty much the only one. Imagine the temptations to vainglory you'd experience, unless you were in the advanced stages of sanctity.

In other words, there would be a HUGE danger of "singularity" or making oneself stand out. Singularity leads to vainglory, pride, and a Pharisaical scorn of our fellow Catholics.

The devil wants us to be proud and vain about ourselves. Some Catholics, giving in to this temptation, look around for "uncharted territory" for something they can do to make themselves singularly holy or even singularly Catholic! Fasting on Sunday sure seems to be a tempting target in this respect.

Yes, just like some Catholics are Pharisees when it comes to what they won't do on Sunday, they end up watching lots of TV on Sunday as that's the only thing that doesn't cause them any scruples -- it can't be considered work, as it doesn't even raise their heart rate.

I've seen posts on Trad Catholic fora "Can I exercise on Sunday?", "Can I play sports on Sunday?", "Can I go out to eat on Sunday?", "What kind of activity can I do on Sunday?" so people are obviously ignorant/confused on the issue. But most of these scrupulous (yet lazy enough to not look into it) Trads agree that watching TV is safe ground. So they -- ironically -- and up watching lots of Hollywood creations on the Lord's Day. The devil must be laughing!

Anyhow, my point is:

It's amazing how many ways you can get it wrong -- how many ways the devil can tempt you to go too far, or not far enough -- while there's just one way to get it right!

One legitimate Sunday fast, as has been mentioned, is the pre-Communion fast, which many traditionalists (such as me!) believe should be from bedtime on the previous day till a significant time after Mass. That is an act of mortification of a sort but also helps intensify the longing to receive Our Lord. For that reason I do know people who go to a later Mass on Sundays.