Nitro Express calibers need not apply. Double rifles are more suitable for these types of cartridges. Anyone wanting a Nitro Express rifle for Dangerous Game would not chose a single shot break action rifle.
Rim diameters from .378 (.223), up to .579 (460 Weatherby), plus 12 and 20 gauge could easily be housed in a moderately sized receiver. This would allow the rifle to be built to house the overwhelming majority of cartridges in use today
Many of us started hunting with break action single shots in 12 or 20 gauge, and although those rounds are by comparison low pressure, the receiver need not be inordinately large to accommodate them.
Single shot options in the marketplace of notoriety in the past 20 years:
Thompson Contender break action single shot, mass marketed - Cancelled due to lack of demadn in 2000.
Dakota Model 10 falling block single shot - Dakota fell into bankruptcy 8 years ago because they couldn't make the math work in relation to demand at $6000 MSRP.
Ruger Number 1 falling block - Bill Ruger had control of his company and wanted a modern replica of the Gibbs Farquarson action. Bill lost money on every single one he made but he didn't care, it was his show and his company. The second he was no longer at the helm of the company, they discontinued the factory configurations. Over the subsequent years there have been Lipsey's exclusives for one distributor, purely meeting the niche demand at an MSRP of around $2500 or double what Bill Ruger was charging for them.
Luxus Arms Model 11 - Probably as close to your requirements of any semi-custom firearm that will ever be made. It was a break action, had bespoke options, a nice array of calibers, and stunning wood. They shuddered years ago because there wasn't enough demand for a break action at their $4000 pricepoint.
This thread has answered your question of why what you want doesn't exist. There isn't enough demand to keep the single shots that we deem "excellent for their purpose" going, much less to create a new offering for an unpleasant to shoot, overbuilt largebore alternative.
Don't hate me, hate the economics. I don't think your wish-list is going to get satisfied unless you get a custom gun built by a maker for over $15k just for your whims, but it will never enter broad production.
P.S. - Your notion that Nitro Express cartridges need not apply solves nothing for you. You cite 460 Weatherby as the top caliber size you'd like. That's 65,000 PSI, you'll never hold it together in a break action single shot, at least not in one that isn't hideously overbuilt. A 470NE by comparison is a meager 35,000psi which you thought would be too big for a single shot break action. (it is, they both are)