The equivalent bike repair to software would be if the bike shop had to fabricate a new part for each repair, down to inventing the metallurgy itself. Would you trust your life to it immediately after that? Or would you make sure it was strong enough first?

In the simple case, the shop isn't really repairing your bike, it's deploying a fix (a new part) that has already been designed and manufactured. This is a much different and easier thing to do.

In the case of new features, let's say you wanted your bike to also attach a kite, so it went faster on a windy day. The bike shop proposes to do this by attaching the kite to a bolt that they want to put in the frame by drilling a hole all the way through this frame. Is this acceptable to do? Maybe, but who knows, really? How much testing do you want to happen before you trust your life that the frame won't collapse?

There's a lot of effort put into engineering things we take for granted every day. The upside to software is we think we can change it to easily do anything. The downside is if you care about reliability then that ten minute / one line change has hundreds to thousands of hours of test program behind it that we collectively pretend doesn't exist.