No, 64-bit audio does exist. It just isn't a format that any hardware natively produces. 64-bit floating-point audio is used as an intermediate format by audio applications for routing audio between plug-ins. Most apps just use 32-bit floating-point audio, but a few apps do use 64-bit.
Floating-point audio has one advantage over integer: it degrades more gracefully. Instead of being linear in nature, floating-point numbers are based on a fractional part and a power of ten. (Think scientific notation.) Thus, larger numbers have lower precision than smaller numbers (but still at least as much precision as 24-bit integer audio). The advantage of this is that when you do something that lowers the overall gain, the extra precision available for small values means lower quality loss. In effect, by using floating-point audio in your effects chain, you can put off gain staging until the end of the process.
That said, it is not currently practical to create a floating-point ADC or DAC. A few experimental floating-point ADC/DAC designs exist in various university science labs, but as far as I'm aware, all commercially-available ADC/DAC hardware operates natively in integer format (generally either 16-bit or 24-bit). It is not at all uncommon for drivers to convert this into a floating-point format for actual use, of course, but the converters are not providing floating-point data, and thus, the precision will never be greater than that of the underlying integer-based converters.