Define better.
More specifically what I mean is that if sleeve valves were any of these on average -- cheaper without regard to performance, higher performance without regard to cost, or lower in cost/performance -- they would be used a lot. Lots of piston automobile engines, boat engines, aircraft engines, lawnmower engines, generator engines, pump engines, and motorcycle engines are made under any of those metrics. Take just a couple of these categories -- cars and motorcycles. There are many examples of those made to be as cheap as possible, ones made as high performance as possible without regard to cost, and ones made with cost/performance in mind, and none or nearly none of them have sleeve valves, and that includes the whole range of engine sizes from radio-controlled airplanes to lawn mowers to motorcycles to cars to construction/excavation equipment to ships to enormous ships.
It also is not a result of design inertia, I can tell you from having worked for several years at Chevy Engineering (the portion of Chevy that was responsible for, among other things, engine design for commercial vehicles, speculative future designs, and for some racing applications such as, depending on the time period, Indy, Grand Prix, and Nascar). There was not huge design inertia -- if it provably worked better for engines, it could get adopted. That's how historically things went from push rods to overhead cam, from 2 valves per cylinder to four, from carburetors to fuel injection, from steel to aluminum, etc. All sorts of engines have been tried out historically in just cars alone -- two stroke, diesel, otto, turbines, electric, hybrid, steam, sterling, inertial energy storage, 8 cylinder, 4 cylinder, V, opposed, Wankel, air cooling, liquid cooling, superchargers, turbochargers, etc., using steel, aluminum, ceramics, plastics, and various other alloys. What we have today is the result of a huge amount of experimentation and optimization.
If sleeve valves were on average better in some way (take your pick of any way at all), I think they'd be used a lot more. If they were better somehow in performance (regardless of cost), you'd see them in racing engines for cars, boats, or motorcyles. If they were cheaper (even if crappy in performance), you'd see them in some car engines or at least some lawn-mower engines or some pump engines. If they were better in cost/performance (where performance could be HP or emissions or weight or gas mileage, etc.), you'd see them in car engines.
