Why "Supports 5V VCC operation" appeared in LVC family datasheets?
The datasheet for a specific part is the law. Some parts in the LVC family were designed specifically to interface between different supply voltage levels, and their specifications will be different than standard logic chips. Your links are to entire manuals so it's difficult to figure out exactly which specifications you are talking about.

The "absolute maximum" supply voltage is the voltage that is likely to damage the device. You must never apply this voltage to the device, even for a short time.

You should focus on the "recommended operating conditions". TI specifies a maximum value for "Vcc Supply Voltage", and that voltage is significantly less than the absolute maximum. Remember this: the part may not function properly and is not guaranteed to meet its specifications and may have a shortened lifetime if you try to use the device outside of those recommended limits.

The term "5V tolerant" usually applies only to input pins rather than the supply voltage. It means that it is safe to apply voltages up to 5V to a specific input pin, even though the device operates at a lower voltage.

At the end of the day there is only one rule. Read and follow the datasheet for the specific device that you are using. If TI changed the datasheet to allow higher voltage operation then they must have improved the design or manufacturing process...they are allowed to improve their parts whenever they want. The why would be pure speculation...

As for the "cons" of using these parts, they are no different from the consideration for using any other part specified for the same operating and maximum voltages. Do not allow voltage spikes that exceed the maximum allowable voltages. Full stop.