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The phrase "have been based" is grammatically correct and can be used in written English.
It is a past perfect tense verb phrase that indicates an action that started in the past and continued until another action or point in time in the past. It can also be used to describe a state or condition that existed in the past and may still continue in the present. Example: The company's success over the past decade can be attributed to its strong values and principles which have been based on honesty and hard work.
Exact(60)
Lifelong marriages have been based on less.
His whole campaign should have been based around this approach.
The public's annoyance may have been based on miscommunication.
NN: Your last four films have been based on novels.
These Tory speeches could have been based on Guardian leaders.
However, the entire scheme may have been based on nothing.
Some may have been based on faulty intelligence.
Your previous films have been based in cities.
But the information was later revealed to have been based on forgeries.
Miliband says recoveries in Britain have been based on the middle.
7.53am: Shock news from Aus, where most of this morning's correspondents seem to have been based.
More suggestions(17)
have existed based
have been analysed
have been centered
have been disaggregated
have been addressed
have been stationed
have been recognised
have been attributed
have described based
have been characterised
have been disseminated
have been premised
have become based
have been headquartered
have worked based
have been established
have been advised
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com