The machine should have two speed settings like Hare and Tortoise. It will only move at 'tortoise speed' (slow) while the boom is above a certain height, regardless of the speed setting.
It's certainly SAFER to move the MEWP at ground level incase a wheel goes down a hole or the ground gives way.
Why not just bring the cage down to move the MEWP if concerned?

The fact that the machine does not isolate and reduces speed considerably whilst basket is raised suggest operationaly yes this can be conducted but the would be a number of process controls that must be implemeted to ensure this is absolutely safe,

Is it safe?

Compared with lowering it to ground level & moving on, it can't be anywhere near as safe.
Having practical experience of this, if you move at height your visability is limited & engaged on so many diffrent levels. You may not be able to ensure there is no conflict with other pedestrian/traffic movements & you need to consider the state of the ground you are moving over - will the operator be thrown for the MEWP if a wheel suddenly digs in?

It is safe. at the end of the day this is what this type of equipment is designed to do. Providing you have adequately trained operators aware of risks whilst operating equipment it is safe.

I did my IPAF Cat 3b (Cherry Picker) ticket and was told on the course that certainly Cat 3a and 3b (Scissor Lift and Cherry Picker) were safe to drive with the cage at height, in fact the machines were designed to be driven and used in that way, the example given to me was a task involving changing a row of lights in a warehouse, it's quicker and easier to just stay at height and drive (at height) along the line of lights changing bulbs.

We were warned about possibilty of reduced vision and in certain circumstances it would be prudent to have a banksman keeping and eye out at ground level.

So it would seem that IPAF thinks it's ok in certain situations with certain precautions.