I remember back in in the late 2000's before a lot of the micro-analytics came about, I did my own 2 season analysis of Henrik and his woes with the puck. The Rangers were having such trouble scoring and I brought up the point that he was a contributor of that by stunting the offensive breakouts. Some took issue with it so I presented facts to back it up.
I found that he was killing 2-4 breakouts on average per GAME (sometimes 6-8!) by either putting his defenseman in horrible positions, reversing the puck in the wrong direction or flat out giving the puck away. Most importantly, during those moments he was contributing to several minutes more of possession for the opposition. I loved Hank, but he was a horrific puck handler. Far below average.
Obviously these weren't perfect stats and the subjectivity of them could be debated, but there was enough data there to show the importance of a good puck handling goalie. If you are average, things seem to even out. But if you are exceptional at it, it can really change things for your team.
Case in point - check out the NHL rule book, rule 27.8.