Sabar,
I do primary fermentation in a 6.5 gallon carboy, rack into a 6 gallon carboy for secondary fermentation, and then rack into a 5 gallon carboy to age. During fermentation I do not worry about headspace as the fermentation is producing a healthy blanket of CO2 that forces out unwanted oxygen. With the last rack, I usually come pretty close to filling the 5 gallon to the neck although at times there will be a "cup" or two of headspace.
Personally, I do not worry about that small amount of headspace as the trap I keep on the batch (even as it ages for several years) makes certain that only the small amount of oxygen (if any depending on whether more CO2 is released after racking) that was present before trapping has a chance to integrate into the must.
I rack into a bottling bucket to bottle where my batch is subject to open air for as long as 15 or 20 minutes. I suppose this could cause harm but haven't experienced it yet.
All of that said, I know that there are wineries that never allow their product contact with ANY free oxygen by pumping everything around with inert gasses. From what our experts are saying, there is likely value in that or they would not do it (hopefully). But as a hobbyist, you need to decide to what level (and what expense, and what changes to techniques, and what changes to recipes) you will go to avoid oxidation.
So far, in my limited experience, a little headroom in the carboys has not caused discernable damage to my batches to the point where I am flushing things with CO2. I'd suggest you try a couple of batches a couple of different ways and see if you notice a difference. Use the techniques that make a difference and don't use the others.
Good luck,
Pewter