Suggest + should
I'm learning about the usage of "suggest", and there is a part of the lesson that is not clear to me. According to the lesson:
"In British English, subjunctive isn’t very common. Instead, British speakers use should + infinitive.
The doctor suggests that he should stop smoking.
The doctor suggested that he should stop smoking.
In direct suggestions that begin with I suggest…, should is not normally used.
I suggest that you get another job. (NOT I suggest that you should get another job.)"
But I know that I've heard a couple of times that people say these kinds of things: I suggest that we should go to the cinema. OR I suggest you should go to the dentist. Then these sentences aren't correct? Can we use suggest together with should, when I am the person who suggests something?
Thanks in advance!