Tell me about it. My 400N split a cylinder head as the camchain went through it like a band saw. You remember the rigmarole: loosen the tensioner bolt, whereupon the camchain tensioner was meant to spring out and tension the chain. Except that it didn't. Cue poking the bolt with a screwdriver to no avail. There were countless Honda models in the 80s with camchain problems. (Not to mention the crosshead bolts made of cheese - but that's another story.)
Desmo valve trains were'nt a Ducati invention, you have to remember that in the early days of motor development, springs were very unreliable and couldn't be manufactured to the tolerances and with the metals there are now. The 1914 Grand Prix Delage and Nagant used a desmodromic valve system, although it bears little resemblance to the modern Ducati offering. The Mercedes-Benz W196 Formula One racing car of 1954-55, and the Mercedes-Benz 300SLR sports racing car of 1955 both had desmodromic valve actuation. In 1956, Fabio Taglioni, a Ducati engineer, developed a desmodromic valve system for the Ducati 125 Grand Prix, creating the Ducati 125 Desmo. He was quoted to say: The specific purpose of the desmodromic system is to force the valves to comply with the timing diagram as consistently as possible. In this way, any lost energy is negligible, the performance curves are more uniform and dependability is better. The engineers that came after him continued that development, and Ducati held a number of patents relating to desmodromics. Ultimately it was originally about reliability as you're not relying on a spring not to fail to close the valve, of course, today springs are as reliable as, but desmo still holds the advantage of being able to control the closing of the valve but at the cost of weight. Now, why belts? While chains and gears may be more durable, rubber composite belts once upon a time were probably quieter, but in most modern engines the noise difference is negligible, are less expensive and more efficient, by dint of being lighter, when compared with a gear or chain system. Also, timing belts don't require lubrication, which is essential with a timing chain or gears. In a nutshell, cost. Belts are cheaper to maintain than a chain. The downside is that they need to be inspected more often and there's the greater potential to snap - even in their service period if for example they start rubbing on stuff or get debris in the belt housing. I wouldn't be at all surprised (and I don't know) if Ducati also moved to chains because firstly it can package the engine tighter, and secondly there is a 'perception' of increased reliability
I remember being fascinated as a schoolboy, learning for the first time how an internal combustion engine worked, and thinking there must be an alternative design to the 'crude' valve, and the energy wasted overcoming the valve springs. It was a while before I learnt about the Desmodromic system and vowed that I would have an engine with that valve system one day. Took me quite a while from that time until I bought my first Ducati though! Interesting video showing 'Valve float' Valve Float - YouTube