Moving from a top 6 Premier League club to Roma is absolutely a step down.
more coli classics ..
and I suppose you think Chelsea were a bigger team than Roma when Jose took over in 2004.
NEWSFLASH - Jose has only ever been at two massive clubs .. Real and Man Utd. Reason? There aren't that many clubs of that size.
His other jobs have been around the Roma level - i.e. Spurs, Porto - with Inter, Chelsea a little bit above that.
That is how it is for coaches who manage lots of European clubs - see Ancelotti, Robson, Hitzfeld, Hiddink, LvG etc etc. That is how it has been for decades.
Those who work their way up and stay at the most powerful clubs are few and far between (Zidane, SAF, Pep so far etc) and they are very much the exceptions.
As a normal-lish human being Jose (and people like him) are unlikely to find the constraints of Germany to their liking so that leaves three big leagues and a handful of teams in each tier.
Stick to NFL / Basketball