For me the Ring Road is fantastic in every way. Have never though of it as ugly or a concrete collar chocking the City, just a very effective and efficient way of getting round the City. Visually it does not offend me in any way and would be upset to see the council dismantle it or mess it around. It's probably one of the very few things the council got right.
It disconnects the city centre from the suburbs both physically and visually, encouraging people to go around the city centre rather than into it;
totally dissuades anyone from walking into the city centre having to navigate the underpasses;
prevents any kind of organic growth of the city centre;
creates large pockets of awkwardly shaped packets of land around it that have always struggled to find a use and are far cheaper than city centre land otherwise should be;
takes up huge amounts of space (it's eight lanes across between J6 and 7);
largely forces everyone towards the centre if they want to travel across the city, especially in the NW where there's no outer ringroad like the A46 and causing long queues on roads like Allesley Old Road and Holyhead Rd because they're not designed to take that level of traffic the RR is designed for with bottlenecks around the single lane sections or bits that people park on outside their houses;
it looks ugly and prevents presenting any kind of vista of the city centre for those entering;
visitors find it daunting having the on/off slipways using the same space and presents them with a terrible first impression;
is becoming increasingly costly to maintain
That's not to say it doesn't have good points - it is pretty effective as a distributor and preventing congestion in the city centre (though as I've said it creates that congestion on the roads that connect to the junctions.
Again, it's something I'm fine with keeping as a route, but it needs rethinking as to how it's engineered for the future.
Biggest missed opportunity in recent years was the Swanswell Initiative that would've made J1-3 at level and integrated into the city much better. Had that occurred I'm certain we'd have seen projects to remove overpasses in favour of at-level or even moving the road into cuttings rather than overpasses in certain areas.