Not all MOSFETs have body diodes but I doubt you can find a power MOSFET which lacks one. It is not a freewheeling diode so much as a parasitic element which may often be used as one. The body diode in early power MOSFETs had a slow recovery time so it was important to prevent it from conducting in high frequency applications.
Like I said, the eGaN FETs are possibly the only power device on the market that actually has neither a substrate junction nor a connection to it. Probably, there are RF devices too.
Interestingly enough, the body diode has always had poor recovery, and as it turns out, necessarily so. The tricks that make good fast-recovery diodes (gold or other "bad" doping, irradiation) are absolute poison to MOSFETs. So you get two basic classes: slow (optimized for slightly lower Rds(on)), and slightly-less-slow (optimized for slightly lower t_rr). Example: IXYS PolarHV vs. HiPerFET series.
Your middle example, the 2N4857, is a JFET (junction field effect transistor) and the diode is an inherent part of the structure connecting the gate to the source and drain. It is unrelated to the body diode found in a MOSFET.
Actually, you can think of the substrate as a JFET gate, and the insulated gate proper as MOS. You get dual control ("back gate") if you put signal on the substrate.
Those eGaN FETs are ultimately built on a silicon die, I wonder how much transconductance you get from it if you scratch away the passivation and make a connection. Would be relevant to dV/dt in high voltage applications (they're up to 300V now). Maybe they thought of that, and shorted it to source or drain?
Tim