I don't know why you'd want to ground one leg of your voltage. I can tell you for sure it can make diagnosing electrical issues much harder when you can't get proper voltage readings between the two legs. And there's no advantage to grounding the common even if it's a true neutral.
I can tell you why you would want to. Its for the same reason neutrals are grounded at the panel in services. Coming out of the power transformer, one leg is grounded - that is what makes it have 0 volts. 0 volts is a good thing when troubleshooting: if you use a meter, you can see if there is potential between a wire and ground, not just the return path. When you see that there isn't potential (voltage), or that a wire is continuous with the ground, you obviously have a ground fault. This is especially helpful when a device fails (internally shorts to case) which is mounted to a gounded item. An example in a car wash would be this: If your meterbox was grounded and bonded to the pumprack where the transformer is, and the transformer neutral (or leg 2 or whatever you want to call it) is gounded, and you have a problem where a keypad or rotary swith fails internally putting power to the meterbox
door, you would have a blown fuse. Hook up a voltmeter to the power supply and see its grounded. Remove one path at a time until you find the circuit open again. Solved - bad keypad or switch or whatever. If it was left floating - you have a hot meterbox which can cause all sorts of electronic problems... The examples are many, but it is normal practice with power mains for safety reasons, but mainly so that a breaker or fuse has a good reason to trip when something goes wrong.
Also, even if you have 208 or 240 feeding the transformer, and have 24vac out, there's not really ever a "neutral". You make a neutral by bonding whichever leg of the transformer that is "common to the loads" to the ground. By doing so, it becomes "neutral" (0 volts to ground). Since a transformer is by definition an isolation device, There is no reference to ground on the secondary (outlet). The exception is an internally grounded transformer where they just bonded it for you.