"I know some hybridizers only assign a number once they decide to keep a seedling for another year."
They say in science, you can never have too much data. They say in science that data is only as good a the accuracy and completeness of the data. They say in science, if you collect the right data you are more likely to achieve your goal or at least know why not. However, many famous scientists were not data collectors in a formal way. They kept it in their brain. We are generally in between. Identify the data that is useful to you and record it.
Dick Parshall recorded the ADS classification of every seedling that bloomed in his garden. It is so much paper that it would not fit into one very large box. The data he kept in his brain was probably more useful to him on this subject. He has said he has never done anything with the paper records and hopes someone will transcribe them to computer data.
Knowing the parents of seedling is some of the best information you can gather. Having said that Dr. Hammett who is a professional plant breeder prefers to combine numerous potential seed parents together in a bed and he selected them for the traits he wanted to combine into his finished product. He lets bees do the pollinating and then grows the seedlings from a nice sample of the plants. He evaluates the seedlings and selects the ones that are closer to his goal and grows only those seedlings the next year abandoning all of the original seed parents. It was a five year process for him and by selecting only the plants closer to his goal(s) each year he incrementally improved the trait(traits) he wanted and had one good plant that was the result of his efforts. All of the seedlings and original mother plants were not kept; no works in progress were kept, only the final product.
Was this method successful because of the data he collected on the seedlings? I bet he kept no written records of the selection process but was one of those "keep it in your head" data people.
Luther Burbank was not much of a record keeper and had a prodigious memory. He was the most successful plant breeder in his time and perhaps of all time. His farm is not too far from Bessie.