Your reasoning is off. I can imagine a team getting 0 shots in 10 mins, which averages to 0 shots in a game, but that will never happen in a full game. For the same reason that Auston Matthews isn't scoring 150 goals this year. (sample size)
2 shots in a period probably happens quite often, but to do that all 3 periods is extremely rare. And you're making basically the same mistake in the second scenario, All that should matter is the 30 shots in 1 period, they don't have to keep it up for 2 more periods.
What I'm saying is this:
If a team manages only to get 2 shots in a period (you yourself said it probably happens quite often, yup) so can it really be a more impressive thing that instead of 20 minutes that feat keeps for 40 minutes more? It could include like post shots or close misses and lots of blocks.
However to shoot 30 times in a period the first thing it requires to happen is that the specific team must have the puck for a long time in that period, not only that it requires that they keep it in the offensive zone, and then it requires that the puck is shot at the goalie. Not to forget that the team has a big chance of losing control of the puck after each shot, if it goes to faceoff the team must win the puck back again.
Also if a team only manages 6 shots, that can include most of this. Can have offensive zone time a lot without getting shots away, can have shots taken but that are blocked etc..
30 shots in 1 period is way more impressive feat.
And about keeping up the pace was not my point, the point was that if you mathematicly calculate then it suggests that 90 shots per game is more impressive and definitely rarer than 2 shots per period. Pure math