Develop to completion may be a squishy word but I understand it to mean the time to produce a nearly max black and full range of available tones. That is my normal practice.
I enjoy sticking my nose in old photography books. With the passage of time and change in materials, dated info gets mentioned on the web which had it's source in older publications. Knowing that, I still point readers to references so they can read for themselves. David Vestal wrote two authoritative books not void of errors. Regardless, David was a great contributor in Popular Photography 35 years ago and still writes for Photo Techniques.
David Vestal posed this question in his book, The Art of Black & White Enlarging. "Does developing the print longer make it richer?" Quote, "Some say so, I've (Vestal) said so myself. But I never tested it objectively before." He went on to develop step tables for 2, 5, and 10 min. Too many of the 10 min tests were stained and he dropped them from further testing. He measured the useful range of tones in each step table print. The useful range (his term) is an approximation of the tones that can be seen distinctly in prints, not getting lost in blackness or whiteness. His conclusion is that the average gain was less than 1 percent and that prolonged print development made no difference in richness that you'd notice.
Richard Henry and Vestal both mention that seldom does adjusting developer dilution control contrast if you let the paper develop to completion. Different print developers (high/low energy) are effective in changing contrast. If you develop for less than 60s it is difficult to achieve uniform development.
From reading it appears there is a slight bump in contast with under exposure and over development. I'm reasonably sure the enlarger light source produces a larger contrast shift. Below is one Vestal quote and paraphrase on printing.
"To get a good print, you first need a picture that deserves one - a picture that's visually alive in some way that can reward a viewer. Most good pictures have fixable faults, and we should make all necessary repairs; but avoid repairs that kill the picture. "
When a paper fits the picture - technically in contrast behavior and tone range; esthetically, in color, surface, and tones - the printing is excellent and nearly effortless.
I like the part about effortless.