This part of a sentence is correct and usable in written English.
This can be used when you want to express that something has been criticized. For example, “The new policy is not without criticisms; many people think it will have a negative impact on the economy.”.
While Cairngorm stakeholders were largely positive from the outset, the model of national park introduced is not without criticism.
To be sure, the use of this instrument is not without criticism.
But, despite their success, TED – and what it stands for – is not without criticism.
While Safety Check is not without criticism, Facebook's ability to harness its uncanny knack for social engagement for disaster relief fundraising is one of the more clear net good results of the world's largest social network.
See Bar-Anan & Nosek (forthcoming) and Machery (forthcoming) for discussion (§2.2.3). 7. The IAT is not without criticism, both for the broad conceptual conclusions researchers have drawn from IAT data (Arkes & Tetlock 2004; Tetlock & Mitchell 2009) and the IAT's ability to predict discriminatory behavior compared with direct measures based on self-report (Oswald et al. 2013).
The process of transplanting music between cultures is not without criticism.
Her appointment, though, is not without criticism about her controversial views on vaccinations and autism.
That research, published in the medical journal BMJ, is not without criticism: According to a report in Bloomberg, there's some dispute about soda sales.
Stansfield's review is not without criticism, conveying disappointment with the plot twist conclusion and also questioning a minor plot hole: why Symphony Angel discards her helmet after crash-landing, thereby breaking off radio communication with Cloudbase.
The call for the integration of mental health into primary care is not without criticism however.
