Tbf there aren't a lot of top managers to begin with, even less when you mix in language skills, playstyle and availability. I mean just right now who would even be generally considered a manager of the highest standards besides Pep and Klopp? Zidane i guess? Simeone, Poch, Allegri...these are already debatable. I'd even say there is no truly fitting and realistically available "big name" coach for Barca to get at the moment.
Finding the right coach is difficult and big names fail a lot too so getting a successful and proven coach that ticks all the boxes is probably not much easier than lucking out with another Pep. Barca aims for a unique style so i don't think hiring on different criteria is a problem and its not like other teams have a way better record of signing coaches anyway, everyone is suffering from the lack of available world class coaches. I mean it wouldn't hurt to get away from.just the 3 things you pointed out but in general i don't think it's generally bad to go for smaller names.
Pursuing a manager can't be done in months. It's a long affair.
Of course, fame and knowledge don't always go hand in hand, and you can find the next best manager with an unproven name. Pochettino, Pep, Zidane, Klopp, all of these were unproven before they got their chance.
Klopp at Mainz wasn't a top name, exloded at Dortmund. Mourinho before Porto was an unknown name, exploded at Porto in 2003-2004. Pep before Barca was unknown outside of the club, Zidane at Madrid was totally un-experienced at this level. Simeone at Atletico again, came from South America and was unproven in Europe.
We either have to go after the biggest names, like Pep, Klopp and 2-3 others, or find an unproven but highly skilled manager, back him full on, and propel him in that category, for a win-win situation. Going for the best is very hard, because the best don't just float around waiting for you to grab them, but are tied to long contracts.
Instead, we're going after 2nd rate C level managers, who lack key things to make it in that category in the future.
Being famous or proven, or tested is a plus, but skill and knowledge are everything (not only skill in tactics, but skill in social interaction, charisma, all of that which is related to leadership, because all elite managers are leaders). We need guys in charge who are able to recognize that.