Fungo,
Great post!
The coach wants catchers who throw runners out. If he throws nearly all runners out the catcher is doing his job.
That said... The scouts and recruiters look to pop times and arm strength as tools that show the ability to throw out runners at the very highest levels of baseball.
The pop time is very much important. Just as the runners time leading off 1B to touching 2B attempting to steal. These are "game" pop times and they're the most important.
The scout or recruiter will always prefer the strong arm and quicker pop times over the catcher who has the weaker arm and slower pop times, even if the slower pop time catcher has the best caught stealing results. In most cases it's the same, but level of competition and level of coaching can make the statistics very misleading. (pitchers who are too slow to the plate falls under coaching)
The best thing that a young catcher can do is work to improve his pop times and arm strength while at the same time maintaining accuracy. The stop watch makes for an easy guide while trying to improve.
Arm strength is perhaps #1, especially if the catcher shows agility and athletic ability. Sometimes we see a catcher with a strong arm but terrible technique. If this player has good feet and overall agility, his strong arm becomes very important in projecting his ability. We know his pop times will get better.