We also have the HM Coastguard, government funded but also with thousands of volunteers who help with rescues. They also operate the UKs SAR helicopters and other assets, so it’s not just the RNLI responsible for sea rescue.
They work in partnership with government assets, similar to the way that most air ambulance charities work in partnership with their local NHS trust.
Most air ambulance charities I’ve worked with over the years actively don’t want to be government funded as they want to retain operational independence and fear that they’d be a low priority for government funding anyway, so can only guarantee the finance they need by raising it via charity contributions.
I’d imagine that the RNLI would feel similarly.