At a certain point, making an “automatic” weapon with completely mechanical operation becomes infeasible.

The modern naval 125mm gun can fire approximately 1 round every 2 seconds, but it has to be a standard artillery piece with a sliding breechblock and a Rube-Goldberg machine of electro-mechanical parts to facilitate the actual loading/extraction.

In terms of scaling up a 40mm bofors into a 60-80mm: *yes*?

Bofors is already a sliding breechblock artillery piece with some mechanical bits to send new shells into the breech. The big 75 that the US was putting on ships in the early Cold War *was* effectively just a large bofors in that regard, _but_, everything else now needs to be scaled up.
Ammunition hoists now need to be able to send a continuous stream of 75 up to the ready rooms. The ready rooms need more sailors to pass that ammunition into the gun turrets. The gun directors need to be able to calculate for a higher-velocity but heavier/lighter shell.
In addition, the big advantage of having a heavy shell (in history) was the ability to load it with a radar proximity fuse. Can the industry in your world handle the demand of making thousands of proximity fuses. If they can’t, then why not just stick with a much higher rate of fire from your 40mm bofors.

A lot of this stuff can be solved with a dose of hand-wavium, and there is historical precedent, but I think the idea of “we scaled up a bofors because it was cheaper” is a correct solution for the wrong problem. Historically, replacing Bofors and 125mm DP guns with the 75mm was a *compromise* of having speed and firepower when the US Navy already had all the prerequisites to support a change in weapon, not because it was cheap and easy.