I’ve been using 28mm tyres on my road bike for a few years now and have found I’m faster (on average) for the same sort of power - not by much but certainly enough to feel it, compared to the original 25mm setup.
I’ve since moved to wider internal diameter wheels with a deeper profile (51mm Bontrager) as opposed to the original mavic wheels (2017 specification Cannondale synapse) and again, this made a minor yet noticeable improvement with the existing 28mm tyres (using tubes).
Then moving to tubeless of the same brand (Conti GP5000) and width again, you guessed it, a small but noticeable improvement - also more noticeable was a comfort benefit, I suspect due to lower pressures.
I’m now about to experiment with running a 30mm on the rear whilst keeping the 28mm on the front.
Hoping to gain some comfort - I’d be surprised if I was able to discern a noticeable speed improvement.
Frame will probably take a 32mm at the most, so no way I can experiment with anything much more substantial.
I’m also a little sceptical that even if the frame could accommodate 40mm, that in the real world environment of average UK tarmac, that it would prove faster.
I think the issue would be the wheel tyre combination - I’d imagine I’d need a wider rim to make the most of the extra tyre width.
Also, although I’m the first to bemoan the state of the UK roads in my area, they are for the most part still relatively smooth, so I’d suspect any benefit cited wouldn’t manifest consistently or frequently enough to make an overall net positive difference?
Would certainly be more comfy and forgiving though on the rough stuff and enable a bit of anxiety-free off roading. 
Interesting concept though. I’d imagine where the roads a consistently rough enough, the benefit would be stronger.