For 22rf the fundamental problem is that most 22rf have a 1 in 16” twist rate. There are already a number of options such as the Norma Eco coming into the market which by reviews seem to be reasonably accurate in normal 22rf. Not superb accuracy but 1” at 50 or 75yards. But they are fast and do crack somewhat.
Given the growing need around the world for an effective and cheap plinking and small vermin round a solution will be found.
What is probably needed is a fast rate twist 22 rf barrel to stabilise a subsonic scintered copper / zinc bullet of about 35 to 40grains. Most 22s have pretty easily removable barrels so this could a simple barrel swap solution, or manufacturers can start producing faster twist rates.
Manufacturers have brought a number of rimfire options over the years. The 5mm Mag was the darling of the early 1970’s. The 22 Win Mag has a small but loyal following. The 17 HMR and 17 Mark 2 have their critics snd devotee’s in equal measure. The market is crying out for lead free capable small bore rimfire rifle. Keeping it as a 22rf is probably the least problematic from a legislative perspective.
Alternatively many 223’s now have fast twist 1 in 7, 1 in 8” barrels. Perhaps an immediate solution would be a subsonic non-toxic load for use on rabbits where silence is needed. This would be an expensive option for factory ammo, but pretty cheap as a reload.
And no I am not a major target shooter, shooting many thousands of rounds of ammo a year. But I do enjoy shooting gongs, and our little club range has a simple sand trap behind the targets. Cost - a digger for a couple of days and a lorry load of sand.
And as for rabbits, my 22 Brno has shot several thousand, but on my current permissions hemorragic fever means we haven’t seen any for many years.
Growing need around the world? How many US states have banned lead ammunition?
My RFD has these on the shelf
Norma ECO Speed-22, he couldn't get them inside 6" at 25 yards in various guns, that is with a 24 grain bullet so a 1:16 should stabilise it.
Rebarrelling 0.22s

£800+ for many guns worth £<150.00!!
Subsonic 0.223, again

, you are going to need a heavy, heavy bullet say 70-90 gr, in lead free at subsonic speeds!! Firstly, .22 cast bullets are used for subsonic as they can be lubricated, copper bullets with that bearing surface may jam in the barrel; secondly twist rate is only half of the stability equation, speed is the other half so you are going to be needing a 1:5 or so at a guess to stabilise long, lead free, 0.22 bullets (I loaded 120 gr subsonics in the 25-45 sharps, 1:10 twist, they literally went through the target sideways, quiet though!); Finally, cost!! speciality 0.223 ammunition is going to be over £1.00 per round, £2.00 the way things are going, who is going to use that for volume rabbit control! Oh, and they will deform less, bounce more, carry more energy down range further as they will not slow as quickly as a deformed lead bullet. All in all a cracking idea!!
The market isn't crying out for a lead free rimfire ammunition because the vast majority of the world is still quite happy to use lead ammunition and will continue to do so.
Your sand trap is exposed to wildlife and therefore could be a risk, you may not be allowed to use it for lead in 2 years time . . . .
You clearly don't live in the real world.