And some horses are pacey the majority of the time, and it can be uncomfortable to ride for much more than short period. Can really get your back hurting.
And whether or not she paces only if pushed too much or not is something you would have to see for yourself.
They may have this horse, if shod, weighted to where the pacing isn't as much of a problem? If you change that much, she might pace more. Or could change toe length and get that too.
But when a horse is pacey? That to me, means one that isn't steady in their gaits, either by training holes, but more generally it is the horse's predisposition to be pacey more than the breeds "saddle gait" be that a shuffle, rack, amble, stepping pace, running walk, or whatever.
If you want more information on how horsemen view it, you can type in search bar, "pacing in gaited horses" "pacing TWH's and how to fix" or something like that.