On the face of it, this is a security matter: government officials discussing the future of this country using accounts which are frequently hacked. More seriously, this is a deliberate evasion of accountability: private accounts aren't subject to Freedom of Information requests, so any government business conducted this way can never be subject to the scrutiny of the public.
Sarah Palin did the same thing - which is why some naughty boy hacked and released her emails, and why media outlets in the US took legal action to examine them. At the root of this is actually a serious philosophical question. In an ideal world, our political overlords are in the job to do what they think is best, secure in the knowledge that the electorate has decided to trust their judgement by voting them in. This should give the confidence to do everything in an open and honest manner.
However, when you see government officials behaving like this:
The FT reports that Dominic Cummings, Gove's chief political aide, wrote to colleagues shortly after he was appointed stating he "will not answer any further emails to my official DfE account …"
The email continued: "i will only answer things that come from gmail accounts from people who i know who they are. i suggest that you do the same in general but thats obv up to you guys – i can explain in person the reason for this …"
then one has to doubt their commitment to the public good. If they were convinced of their altruistic motives, they wouldn't move discussions into private, unaccountable spaces. It gives me a strong whiff of not quite guilt, but certainly awareness that the kinds of things they're up to - in this particular case inventing a special class of schools run by and for their political and social allies - are not in the best interests of the country, and automatically require evasion and dishonesty to achieve their aims. This isn't corruption in the classical sense of filling one's own bank account, but it's clearly moral and political corruption of the most corrosive kind.
It suggests that they consciously see government as a vehicle for their private interests, a fat cow to be milked for selfish gain rather than used to feed the masses: in a very real sense, this is class warfare from the top. There's no principle involved here: like Palin, they publicly denounce government as an oppressive enemy of individual enterprise, while distorting its authority for their own purposes. They've captured the government and they're going to extract every penny they can for as long as they're there.
In Kenya, political corruption is so institutionalised that one incoming government minister announced that the new regime merely wanted its own turn at the udders: 'It is our turn to eat', rather than cleaning up the system. I can't see any difference between that and the hole-in-the-corner corruption of the Goves and Palins, other than the Kenyan minister's honesty.