My high Karma character has a literal army of contacts at 80+. And most of them are connection 1 or 2. The fact is you don't really need more then that for the majority of contacts to be useful.
Sure, you want a select few at very high connection ratings... Your Fixer, your regular Fence, maybe even a Smuggler for when things get hot and you need to beat feet to an other continent (hey! It happens!)
A rating 2 wage slave in the accounting department can tell you where a VIP likes to shop, just by checking records....
A rating 2 Bartender may know your mark likes dirty vodka tonics and Blondes....
A rating 1 street kid can still run messages and packages for you.
And most importantly of all: Cross checking facts and stats among a horde of contacts yields more results then going to just 2 or 3 high connection contacts.... yet cost you the same amount of Karma.