Why is it or isn't it advisable/smart for a healthy individual to simply remove suspicious skin spots himself/herself?
The Mayo Clinic published a slideshow aimed at helping people identify possible melanomas. Take a look at it. Do you think you'd be able to successfully differentiate between a melanoma and a benign "suspicious skin spot" every single time? Now consider that melanoma is just one of many different types of skin cancer, and that skin cancer is by far the most common type of cancer.1
One particular advantage we have in fighting this type of cancer is that it often comes with a warning sign, the "suspicious skin spots" you mention. And this is extraordinarily important in successfully fighting the disease. In 2014, 46% of skin cancer patients in England were diagnosed in stages III or IV, which often means death for the patients. One of the single most crucial factors in whether or not a cancer patient will outlive the cancer is early diagnosis.2
The suggestion of just removing suspicious skin spots as you notice them is thus enormously dangerous, because by the time you notice the spot, you could already have metastatic cancer. Indeed, 52% of non-Hispanic black patients and 26% of Hispanic patients receive an initial diagnosis of advanced stage melanoma, as do 16% of non-Hispanic white patients. Note that it is unclear from the source whether this statistic applies specifically within the general population of the US, the general population of the world, or what have you.3
In a type of cancers so common that an anticipated one in five US residents will get some form of skin cancer at some point in his or her life,4 wouldn't you agree that any step that can improve survival rate as drastically as having a doctor check your suspicious skin spot is most decidedly a step well worth taking?