I'd say that it also depends where your Eagle flight is coming from. In winter flights from SFO-LAX are horribly weather-affected – no problem on a nice dry day, but low clouds and rain and southerly winds can lead to the LAX flights being cancelled and badly delayed.

Secondly it depends where you are going internationally and what the alternatives are if you are late (for example, London has 5 flights a day on AA / BA, but I don't know about other destinations).

In simple terms, if you can book the ticket then it must be a legal connection and so they will look after you, but the fact that it is a legal connection doesn't mean the same as a guaranteed connection.