Another turn of your question would be 'Do you want your best work being appreciated by your peers all over the world'? No, or yes?
You could hide behind impact factor publications that your organization has to pay a huge amount of money to get access, after they have paid for your funding to carry out your research. I don't want that. Science, as I understand, is about sharing ideas, not Apples (or money, patents).
There are two problems: (1) predatory OA publishers, who lure researchers into publishing with them for making their own fortune, and (2) organizations that are focused on impact, which is not always to get with OA publications.
But you have to ask yourselves: What is impact? Is it really the citation statistics of journals, or rather the number of people that read, digest and use your ideas laid down in your papers?
It depends... everybody can read open access journals but due to many predatory publishers, their reputation is not good among lots of researchers. So, publishing in other journals (that do not charge authors but charge readers) can have a higher impact as all good univeristies have bought all the main databases, anyway, and non-academic people usually do not read academic papers. Also, for career advancement and increasing the chance of getting research financing, it is good to get published in indexed journals (by Web of Science or at least Scopus) or journals that your country/university considers relevant. My most-cited paper (about case study methodology in international business) was published in an open access journal but it has been cited by only a few people in my field.
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