Twin brothers eating the same diet, working at the same job. Three times a week for the next 52 weeks, both brothers undertake a progressive resistance-training program, each adding weight, sets, or reps in a logical manner over the whole year. One difference: the first brother does deadlifts only. The second brother does arm curls only.
After a year, who do you think will have bigger arms? Obviously it will be the first brother, who put more overall stress and load through his system. Even though he didn't bend his elbow at all.
The bottom line is that muscle growth is a systemic issue, not a localized one. If you put a stress on the forearm only, of course it would grow, but that growth would be limited because the systemic load is small. If you did deadlifts, on the other hand, the systemic load would be so big, everything would grow.