When writing scientific articles, I often feel that, for example,
Note that the model can be solved exactly.
The model can be solved exactly.
are equivalent. Other, similar phrases that are often used but seem to be not strictly necessary include "let us mention" and "let us point out". While including such phrases makes the language a bit more personal and engaging for the reader, the longer sentences may outweigh these benefits.
I would appreciate some guidance regarding when to use such phrases.