"He already has, in practice, all the power of the unelected head of state"
B.J. is an Elected Head of state. He won his mandate in a very clear and unambiguous election, the primary issues of which concerned not only on his leadership and tenure, but also the pivotal issue of Brexit. The election had very high participation rate, and the UK public was very well informed with respect to the stakes involved. B.J. doesn't have absolute power and both his party and opponent MPs can challenge his authority.
The EU meanwhile, has barely any democratic legitimacy.
The President of the Commission and members of the Cabinet - those that enact legislation - are unelected.
Ursula Von Der Leyen did not stand for election. She was plucked from obscurity by Macron and Merkel after the EU elections, in a closed, backroom deal in which voters had no effective influence. The protocols by which she was chosen are not codified, in fact, it's only recently agreed to (Treaty of Lisbon) elected MEPs should even have to be consulted.
Von Der Leyen was not introduced to the public before the election, she didn't go on a media circuit so as to be introduced to the public of various countries where people could learn about her or her platform. There were no editorials, there was no media vetting, there were no interviews, there was no pragmatic by which voters could even learn about their would be leader. She was imposed in EU voters, probably less than 2% of whom had even heard of her.
EU elections have very low rates of participation, EU voters have very low awareness of any of the material issues, MEPs have very little ability to influence legislation and very limited ability to censure leaders.
So yes, Boris Johnson (and Macron, and Merkel) have considerably more legitimacy than any members of the EU apparatus, and that might very well serve as a better basis for European citizens to influence the establishment of rules or laws via treaties as opposed to the very indirect democratic mechanisms of the EU.