I have registered several plants but only introduced a couple. I gave samples of my plants to a friend with a commercial nursery to evaluate. After being grown in a commercial operation, several plants showed weak traits. It's disappointing, but I think many of the smaller hybridizers need others to evaluate their plants. We tend to be more accepting of faults than others will be. I would not register something solely based on someone else's opinion, but I would consider it. Everyone has likes, and if I start hybridizing for someone else's likes, I'll probably never reach the goals I have set for myself. I know my wife can walk the seedling beds and never see a cull.
I appreciate and respect the listing of parentage provided by some hybridizers. I have tried to be as diligent, but after hurricane Ike dealt me a blow and then some health issues, I have plants with unknown parents, or some I'm not 100% sure of. Some are pretty good plants, and I will not throw them away. I think as much as the parentage of the plants, who the hybridizer is, is also important. I will accept a plant with unknown parentage from some hybridizers.
In the case of having to label long crosses, I try to hold to a rule of mine; if it is worth crossing, it is worth assigning a seedling number. I have never selected more than 99 seedlings in a year, so I find a 4 digit seedling number is adequate for seedlings. Last two digits of the year followed by seedling number. So I should never have a cross requiring more than AAAA X BBBB. I do make an exception when two or more seedlings with the same cross are selected. I add A, B etc. to the number.
I agree with the comments about in-breeding and line breeding. It is neither good or bad, but can be both. We would not have the wonderful forms and patterned flowers we have today without it, but it also has its dark side. Just as conversions, it will concentrate traits. Some not readily apparent. Trying to achieve a result too quickly usually has bad consequences.
If you have a plant you really like, give it a chance to disappoint you. Line it out in different locations. Give it different watering regimens or levels of care. Then if it's still around in five years or so, and still impresses and pleases you, consider registering it. And then if others like it too, maybe introducing it.
Good luck, Ed
