Since your crossovers are most likely second order 12db/octave, or higher, even if the old capacitor in the tweeter leg shorted out, your choke coil in parallel with the tweeter would act as a shunt to the low frequencies (similar to a series style crossover) and drastically reduce the bass going to both the tweeter AND the woofer. So, if any low bass gets to the woofer, you know the cap in series with the tweeter is at least doing something, and the tweeter is protected.
This would not apply to 6db/octave crossovers at all. If a series cap in a 6db/oct shorts out, you get full bass to the tweeter and that's usually fatal.
Ken