you are mostly correct. but i wouldn't go as far as to say that "abrasive force" is needed. in fact, most tooth brushes, including soft ones are far too hard and abrasive. the vast majority of people brush too hard, which actually can cause recession, bone loss, and loss of tooth structure on the front surfaces of the teeth. use an extra soft toothbrush, and be thorough, but DO NOT BRUSH HARD. 45 degree angle / \ on the top teeth and \ / on the bottom teeth, smooth circles and involve about 1mm of gum tissue, but again, DO NOT BRUSH HARD. spend a good two minutes doing this. regular toothbrushes are only inferior to electric due to the operator of said toothbrush not doing it correctly, nor for the appropriate amount of time.
alternatively use an electric tooth brush that can (a) tell you if you push too hard, and (b) time you to make sure you do it for 2 minutes.
As for toothpaste, in my opinion it is a adjunct to brushing and flossing. tooth paste will certainly help make your breath smell better, if it has fluoride in it it will certainly help with cavity prevention, but it is not an analog to soap, at all. brushing without toothpaste is, in most cases, almost as good as brushing with a toothpaste, but everyone is different.
going to the dentist is essential because it's basically impossible to get all of the plaque removed from your teeth with brushing and flossing, you always leave things behind, and the plaque calcifies and sticks to the teeth, and at that point is not easily removed (ie, you need your hygieniest to scale it off). calculus ("tartar") harbors bacteria and exacerbates the process of gingivitis occurring, this can then transition to something far more nefarious where you lose the bone that holds your teeth in.
there are like 10 factors that can lead to tooth decay, and the same can be said for periodontal disease. genetics, the makeup and amount of saliva you produce, how hypotonic it is, the pH of your mouth, medical conditions and medications, the typical microbiota that are in your mouth, the makeup of your enamel and how strong it is, the anatomy of the teeth and mouth and the alignment of the teeth (ie. orthodontics is not just for looks). how well you brush and floss, how often you go to the dentist. notice that only a few of those factors can even be controlled or taken into account. this is why unfortunately we have to be reactive to problems in many cases rather than proactive. especially when most dental problems (cavities, gingivitis and periodontitis) come with NO SYMPTOMS whatsoever.
TL DR; mechanical removal is far more important than ttoothpaste (brushing, flossing), but fluoride toothpaste is a good idea
oh yeah, i'm a dentist btw