Is it a good idea to coil long spare patch leads inside the cabinet?

Not usually.

A modest amount of neatly managed slack is useful. Large coils of unnecessary patch lead consume space, complicate tracing and can gradually turn an otherwise tidy cabinet into a thicket of cable.

If a device half a metre away is connected with a 10m patch lead, coiling the remaining 9.5m beautifully doesn’t alter the fact that you’re storing approximately one small room's journey inside the rack.

Use a sensible lead length where practical, and manage whatever slack remains.