Motivated by prior expectations that Kerr-induced distortion limits squeezing in degenerate parametric amplifiers, we varied external flux and pump power to explore operating points where Kerr nonlinearity is theoretically minimized. We find that for practical applications where the squeezing frequency is fixed, the Kerr was variable by about a factor of two and the achievable squeezing showed no significant dependence on Kerr. Theoretical modeling supports this observation and indicates that baseline Kerr values in state-of-the-art SPAs are already too small to impose a practical limitation. Instead, squeezing was dominated by internal resonator loss and insertion loss in the microwave chain. These results indicate that, in practical SPAs, reducing loss, rather than suppressing Kerr, is the primary route to improved squeezing performance.