Because himself does not mean the same as his. "Frantisek is looking for the car himself." means Frantisek himself personally is (also) conducting the search.
Also you can have "Frantisek himself", that is very different from "his Frantisek".
the svuj pronouns are not just for "my" then? is it for anyone except "your?" (his, hers, theirs...) how do we know here that sve is for "his?"
Svůj is for any possessive adjectives INCLUDING yours, but the owner must be the subject of the sentence (as is František in this sentence). See also the Tips and notes.