Historically the Japanese depth charges were designed according to WWI specs, and they were unaware that US fleet boats could dive deeper than 150 feet. That was until sometime in 1943 when a jerkoff congressman named Andrew May blabbed to the press that American subs had a good survival rate because the enemy was setting his depth charges too shallow.
Historically I suspect the count was (1) for tactical info, if you knew how many they had to start you could safely go up to periscope depth and attack with torpedoes, and (2) for strategic info, assuming you survive the attack the brass might be able to make some use of the info regarding their ASW tactics.
Myself, I don't hang around to count - when the first torpedo impacts I go to flank speed and kick out a decoy while heading for test depth, when I reach 250 feet I go to slow speed and silent running. Then I use the compass to draw a five mile circle around myself on the chart and head for the outside of that circle. It's very rare that I get detected creeping away at 1 knot for five hours, especially with the tactic of kicking out a decoy and going full speed away from that decoy for the five minutes it takes to get to 250 feet - they initially focus on the decoy then start their search in that area, but by then I'm more than a half a mile away from where I started. Going straight ahead works best since you're crossing under what's left of the convoy or task force to the other side, so whatever noise you make during the initial sprint will be lost in the other noise.