Like who, lol. Name one. Fergie treasured it and to this day Keane goes on mild rants on ITV on how pussy and impassionate players have become about it since they started crashing out and couldn’t cut it abroad anymore. Any manager who thinks a trophy basically making you the best team on the continent that year is not special, is a moron. It is universally the most iconic televised sports competition on the globe. It’s how many of today’s iconic clubs got famous like Liverpool. Only the major internationals carry more prestige.
Of course they view it as special, but not to the absurd level fans view it as to make an obsession of not winning it. And it's true managers and big teams don't usually prepare for CL in a special away except Madrid. Madrid have won the CL a lot of times, but in a lot of those times they kind of focused only on the CL while taking it easy in the other competitions, finishing, 3rd, 4th or even lower in La Liga in those seasons. This is a big asterisk sign, as it's a lot easier to not have to fight on multiple fronts late in the season when tired legs start to appear. If you look at United under Ferguson, they won it two times in years where they also won the title in England. Bayern, the same, 2001 and 2013 Champions in Germany as well. Barca have won it 4 times in a little more than a decade as part of double or treble. Madrid just 1 out of 12 wins has them winning the league that season.
So the CL is special, but when you sacrifice a league season as to be more fresh and mentally charged to win it, you clearly as a club value it more than other teams do. So, it can't be denied that Madrid is kind of obsessed with the CL in ways other teams aren't.
Also, the winning the CL doesn't make you the best team on the continent. It's very easy to contradict that claim, as I'm sure you know it already.