Bug introduced in 10.1 or earlier and persisting through 11.0.1 or later

When I use the following command to plot a graph:

Plot[x^Gamma[x - 1], {x, 0, 1}]

or:

Plot[x^Gamma[x - 1], {x, 0, 1}, PlotRange -> Automatic]

it works fine.

If I use:

Plot[x^Gamma[x - 1], {x, 0, 1}, PlotRange -> Full]
Plot[x^Gamma[x - 1], {x, 0, 1}, PlotRange -> All]

Edited: 25.05.2016

Plot[(x^6000 - Sin[x]^6000)/(x^2*Sin[x]^6000), {x, -10, 10}, PlotRange -> All]
Plot[(x^6000 - Sin[x]^6000)/(x^2*Sin[x]^6000), {x, -10, 10}, PlotRange -> Full]

it does not show any Plot(Invisible Plot)!

I have: (* MMA 10.2.0 for Microsoft Windows (64-bit) (July 7, 2015)*)