'unexceptionable' is correct and usable in written English.
You can use it to describe something that meets all of the accepted standards or is free from criticism. Example: His apology was unexceptionable, so everyone accepted it.
Dictionary
unexceptionable
adjective
Beyond reproach; unimpeachable
synonyms
Exact(53)
Its stated revenue-recognition policies were unexceptionable.
It was an example, he said, of the intolerance of the secular world when confronted by outward displays of religious faith.Taken on its own, the primate's sermon was unexceptionable.
In other words, Mr Havel spun a good line in well-meaning and unexceptionable waffle.Few people doubt that Mr Havel, who since the fall of communism has presided first over Czechoslovakia and then, after the country split in 1993, the Czech Republic, is a great man.
Most of his ideas were unexceptionable: more bicycle paths, safer routes for children to walk to school, a single national telephone number for bus and train information.
This, though unexceptionable, was seen as yet again avoiding the painful essence of Holocaust expiation and was compared unfavourably with Pope John Paul II's prayer in March 2000 at the same spot.Islamic clerics escorted the pope to the Dome of the Rock in Jerusalem (shown above), to Bethlehem and to Nazareth.
Mr Najib has since agreed to a parliamentary committee to look into the demands, which are mostly unexceptionable: to clean up voters' lists, allegedly swollen with "phantoms"; to extend the election-campaign period, at present just seven to nine days; to tighten up the postal-vote system; and so on.
Nationally, the ratio for children up to six years of age rose from a biologically unexceptionable 104 in 1981 to a biologically impossible 108 in 2001.
This entails such unexceptionable measures as investing in infrastructure and research and development and giving small enterprises access to credit.
This has affected the budget in the most unexceptionable way.
Similar(2)
We started with the unexceptionable-sounding thought that moral and evaluative judgments are intended to guide conduct; we arrived at a blanket denial of the possibility of akratic action which fits ill with observed facts.
Black insists they were 'unexceptionable payments, insufficiently documented' and that there was 'no evidence of impropriety'.
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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