I don't hang around clay shooting grounds much so don't know what's considered cool to shoot with here in the UK!
Admittedly my shooting is in the privileged bracket, driven shoots with mostly similar aged people (50s-80s). The predominant gun is still the English side by side, over and unders being rare, though no longer 'frowned upon'.
Most of my shooting friends have passed on English - or Scottish - side by sides to their sons. Like their fathers, they started in the field in the beating line before being allowed to carry a gun.
I know we are now probably in a minority, but it offers a glimmer of light for the future. Of course, with continued regular shooting some of those side by sides will eventually need either retiring or re-barrelling, as most of them have already or will shortly approach their 100th year. Perhaps, in years to come, the available pool of fine side by sides will diminish to the point where, following the laws of supply and demand, their value reflects collectable, rather than usable, status.
The other factor we certainly have to consider here is the possible total banning of lead shot. Of course we simply do not want to be putting steel down our old and 'delicate' barrels; bismuth remains an expensive alternative. We would rather keep with lead.
Tim