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EDIT: it occurs to me that an alternate property could be: a positive ternary form will be defined to be fungible if its sporadics are all composite. Or perhaps funicular.

EDIT TOOOOO: I thought I might find examples of forms $x^2 + m y^2 + n z^2$ that seem to be fungible, or perhaps funicular, despite lacking proof. The first example is $$ x^2 + y^2 + 48 z^2 \neq 21 \cdot 9^k $$ compared with the other form in that genus, $2 x^2 + 2 y^2 + 13 z^2 + 2 y z + 2 z x,$ checked on numbers up to 1,250,000. Very similar, $$ x^2 + 4y^2 + 20 z^2 \neq 77 $$ compared with the other form in that genus, $4 x^2 + 4y^2 + 5 z^2,$ also checked on numbers up to 1,250,000. In this second case it is easy to show that each form of the genus represents 4 times any number represented by the other form, and no numbers $2 \pmod 4$ are represented anyway, so only odd numbers come up. Anyway, 21 and 77 are composite. I have not proved these completely, just checked on computer.

EDIT: it occurs to me that an alternate property could be: a positive ternary form will be defined to be fungible if its sporadics are all composite. Or perhaps funicular. I looked it up, the best would be frangible.

EDIT TOOOOO: I thought I might find examples of forms $x^2 + m y^2 + n z^2$ that seem to be fungible, or perhaps funicular, or frangible, despite lacking proof. The first example is $$ x^2 + y^2 + 48 z^2 \neq 21 \cdot 9^k $$ compared with the other form in that genus, $2 x^2 + 2 y^2 + 13 z^2 + 2 y z + 2 z x,$ checked on numbers up to 1,250,000. Very similar, $$ x^2 + 4y^2 + 20 z^2 \neq 77 $$ compared with the other form in that genus, $4 x^2 + 4y^2 + 5 z^2,$ also checked on numbers up to 1,250,000. In this second case it is easy to show that each form of the genus represents 4 times any number represented by the other form, and no numbers $2 \pmod 4$ are represented anyway, so only odd numbers come up. Anyway, 21 and 77 are composite. I have not proved these completely, just checked on computer.

EDIT TOOTOOTOO: I got an opinion from Jeremy Rouse. He points out that any positive ternary has two possible causes for having infinitely many numbers missed (compared to its genus), those being high divisibility by anisotropic primes or spinor exceptional classes. These two phenomena affect only finitely many squareclasses. In both cases, we do not increase the set of primes missed, with the result that a positive ternary fails to represent only a finite number of eligible (by congruence conditions) primes. This also explains, to some degree, the reference to Duke and Schulze-Pillot (1990). The final corollary says that any sufficiently large number that is primitively represented by some form in the same spinor genus is represented by the form of interest. There are only a few spinor exceptional squareclasses, so, even in an irregular spinor genus, we can only miss finitely many squarefree numbers, as those other than the spinor exceptional integers are represented by something in the same spinor genus, and primes are squarefree and therefore represented primitively if at all. I think I've caught up now. Note the D_S-P results give no effective bound, so we cannot identify the primes missed without some fortunate accident such as regularity, spinor regularity, regularity with regard to all odd numbers, and so forth.

EDIT TOOOOO: I thought I might find examples of forms $x^2 + m y^2 + n z^2$ that seem to be fungible, or perhaps funicular, despite lacking proof. The first example is $$ x^2 + y^2 + 48 z^2 \neq 21 \cdot 9^k $$ compared with the other form in that genus, $2 x^2 + 2 y^2 + 13 z^2 + 2 y z + 2 z x,$ checked on numbers up to 1,250,000. Very similar, $$ x^2 + 4y^2 + 20 z^2 \neq 77 $$ compared with the other form in that genus, $4 x^2 + 4y^2 + 5 z^2,$ also checked on numbers up to 1,250,000. In this second case it is easy to show that each form of the genus represents 4 times any number represented by the other form, and no numbers $2 \pmod 4$ are represented anyway, so only odd numbers come up. Anyway, 21 and 77 are composite. I have not proved these completely, just checked on computer.