More than any other tool in the kit, a reliable lever makes changing a tire easier, especially if you have road bike tires, which are difficult to remove. However, throughout testing, levers seemed to be the one item more prone to failure and poor design than anything else. For example, I found a random orange lever floating around my basement and I threw it in the test pool for fun—it seemed solid enough … until I began prying at the rim of a tire. It bent directly in half, slowly and smoothly, like taffy, and then was boomerang shaped forevermore.
On the other hand, an on-bike repair kit will be a much smarter selection of tools that you are most likely to need. You should figure out the type of screws that are fitted on your bike and the things that are most likely to go wrong on a ride. Address only these things so as not to burden yourself too much with unnecessary stuff. Moreover, there are bike repair kits used on long rides and those used on shorter rides. The longer the ride, the more tools, and spare parts you will have to bring unless you want to have a very long hike back home.
Modern bottom brackets use a sealed bearing type construction that keeps water and debris locked out, so they seldom go wrong. Maintenance is impossible so they need replacing when they do wear out. Older style cup bottom brackets need to be re-greased every now and again, and occasionally will need to have their bearings replaced. There are a lot more teeth on the chainring cogs than those on the rear cassette, so need changing less regularly. Cranks usually a solid one piece construction so there is not much to go wrong.