Yet why will this same person be able to consistently meet obligations at work or with family even when they don't feel like it? Would it be it fair to say that this willpower/motivation deficit is curiously selective?

Like belly buttons, motivation falls into two broad categories, internal and external.

External motivation is where we act in order to receive the approval or avoid the disapproval of others. Relying primarily on external motivation means that control of our lives largely exists outside of ourselves.

Internal motivation is where you are striving to excel, often for no other reason than for challenging and bettering yourself, although you may also very well please others in process.  You are in a sense "the boss of you."

Our culture pays lip service to the idea of being a "self-starter" yet we are mostly conditioned to respond to external motivation and to be "average."  After all, what would happen if everyone just started thinking for themselves?

Here is a fable about the two motivational styles.  Milton hated going to gym class as a kid and only participated at a bare minimum. The grading pen of the gym teacher was a source of external motivation and he wouldn't have attended at all if he weren't afraid of what his parents would do if he failed-yet even more external motivation.

After his school days he religiously avoids any strenuous activity. At middle age he is encountering health problems because of his couch potato ways and his doctor tells him flat out to that he needs to become more active or his condition will deteriorate further.

Milton begrudgingly starts to take up exercise but harbors a lot of resentment because his doctor is "making" him do this. After a short time he gives up and his health continues to give up on him!

His sister Virginia was not that fond of exercise either when she was younger.  Eventually though she decided that if being physically active would enable her to remain youthful and more attractive, then she was going to give it her level best. In the process she also sidesteps the health problems that befell her brother.

As you have probably guessed, self-improvement goals require strong internal motivation or what is frequently described as self-mastery. You accept greater  responsibility for the direction you are headed for and develop skills and traits like prioritization, time management, impulse control, patience, persistence and clear intention.  It does take some courage to chart your own course, however this is really the true "secret" of all high-end achievers.