Very nice idea.
The only bad thing is that occasional visitors (who only visit the site after 90 days) do not benefit from the security mechanism HPKP. But possibly you do not have many of such visitors, so that this does not matter.
Just keep in mind that the certificate lifetime might be reduced below below 90 days in the future, so in this case this might be more important.
But generally your idea is really nice. To have this automated - preferable in the official LE client - which would also automate the HPKP header configuration is really a wonderful idea. This way HPKP would get much simplier.
The thing is: It's as risky as before. That's why the LE client obviously still has to generate backup certs. This is no problem, but it somehow has to convince the administrator move these backup certs off the server (at least one of them) and store them somewhere securely else. That's where the automation ends.
However this could also be simplified very much by creating enough backup certificates for, say... one year, storing the pins and telling the admin to put them somewhere else. Afterwards the client could just use the (pregenerated) pins (aka hashes) and put them in the HPKP header. Additionally it should inform (mail) the admin the currently used backup key so he is able to use the right one in case he is not able to find this out later.
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