No, never saw the Stuart Smalley bit. Of course it's more complicated than that -- James was referencing just one connection between thought, emotion, and behavior. His idea works well when the object or person is not actually dangerous but is
imagined to be dangerous. Scratching the ears of a big snarling dog is likely to get one's hand bit off. Fearing all dogs, because one imagines them all to be dangerous, would be reduced by interacting with friendly dogs.
It turns out that if your self esteem is low enough, positive self talk can actually have a negative effect. — Reformed Nihilist
I don't want to defend the often vacuous self-help industry, but there is
some truth to the notion of positive self-talk and visualization of a desired action (like visualizing pitching a baseball perfectly). Probably not a lot of truth, just some truth. 25% truth/75% baloney.
But getting back to the OP's problem: One can decide intellectually--to will--that one
will care about people more. Say, one decides one ought to be more caring about homeless people. We can not just throw a switch, producing the fact of an emotional caring for the needs and suffering of the homeless. One has to involve one's self at some level with people who are homeless and interact with them.
This is a place where James' idea can work. By interacting with homeless people AS IF they were real people who might be interesting as well as unfortunate, we can develop emotional connections. (Of course, this can backfire. A homeless person can, like any other person, be intensely disagreeable.)
By interacting with homeless people, one can establish the necessary emotional connection to actually care.
On the other hand, one can be blinded by emotional connection.
Take the case of illegal immigrants and refugees. Some (maybe many) of the advocates for these groups of people have an intensely strong emotional connection. This can interfere with a more comprehensive view. Immigrant and refugee advocates sometimes can not see contradictions -- like opposing an effort to reduce human trafficking. "Cracking down on human trafficking will break up families." Trafficking wouldn't be going on if the families weren't already broken up, and human traffickers are NOT on the side of refugees or illegal immigrants. Traffickers are on the side of easy money, sometimes at the cost of the lives they are trafficking in.
Similarly, people who advocate for users of illicit drugs ALWAYS object to tighter enforcement and control of drugs because "that will just drive drugs users underground". Well, they already are underground, and are dying because of drug use, not because of law enforcement.
Another example of blinded advocates were gay men in the late 1970s and early 1980s. They were emotionally too close to the problem to recognize that some of their gay sexual behavior was causing very significant health problems -- even before AIDS appeared in 1981.
UPSHOT: It is necessary to have emotional involvement to care, but too much emotional involvement can interfere with perception, just as no emotional involvement can interfere.