I just spent 30 minutes trying to reconnect my chain.

I needed to take out a few links, I popped out two pins using the chain tool, took one of the pins and tried to push it back in. This is an extremely delicate work, to put it mildly. The pin is just thick enough that I can't push it into the hole by hand. I need to hold the chain sideways, balance the pin on top of the hole, put on the chain tool and try to push it in. The pin is slippery and tends to fall to one side from any vibration. Even if I manage to squeeze it between the chain tool and the chain, 9 times out of 10 it goes in crooked and I have to start over.

I can't imagine doing this at the side of the road in the event of a malfunction. More to the point, I can't imagine a mechanic doing this in a bike shop. I have a SRAM 10-speed chain and I can buy new "master links" which cost $16 for a 4-pack on Amazon (which is unreasonable since I can get a brand new chain for $27). My chain tool (Park Tool CT-5) does not seem to offer any functionality that would make pushing pins into the chain any easier. What am I missing?