You seem to have some pretty fundamental misunderstandings about strength training. Even very intense programs can be undertaken without turning into an immobile blob of muscle. Strength is gained not only through hypertrophy but also through neurological changes, particularly those related to motor unit recruitment. Technique is also critical and fixing flaws there can lead to large improvements.
>I have 2 friends who bulk up and are actually in a very bad shape mobility wise, their arms are so big that they can't reach arms behind their backs
Bodybuilding is only one type of strength training. Furthermore, the primary goal of bodybuilding is aesthetics, not necessarily strength. That's not to say that they're not strong, but there's a reason why body building competitions will involve flexing in front of the judges while olympic lifting competitions won't.