We could grow the Bitcoin economy and have more businesses run on the Bitcoin standard if we could somehow get them to constantly carry out business transactions on the Lightning Network rails without any need to convert to Fiat?

This is exactly what the Fiat channels protocol proposes. Complete independence from interacting with Fiat rails or stablecoins. There's no one point of failure, and it is censorship resistant, since anyone can run a Host (no reliance on any particular company to offer Host services). Hence, businesses with enough financial capacity can actually self-host.

Easy community Bitcoin banking that ensures that people who have a fixed cost can still comfortably transact and live on the Bitcoin standard without worries about Volatility. Keeping the majority of their earnings in a self-custody Bitcoin stack, while living their normal lives, spending hedged-Bitcoin Fiat IOUs.

Sats keep exchanging hands while the surface value is Fiat. Anyone tired can instantly sweep back to normal Lightning rails and become fully self-custodial again without needing permision.

With a proposed "proof of reserve and hedging capital" protocol, public Hosts that may want to offer the services as community banks can, at all times, be independently scrutinized to ensure absolute commitment.