There would be no Very Big Hole in the ground. There WOULD be a lot of little holes in the ground.
There has already been considerable drilling on federal ‘wilderness’ lands in the lower 48 and Alaska’s North Slope; the question here is whether Alaskan wilderness under discussion is more environmentally sensitive than other areas.
Creating a typical ‘pad’ for a land rig involves clearing and leveling a rectangular patch covering a couple of acres, plus an access raod from the nearest existing highway.
As I understand it, the immediate concern about environmental damage in Alaska pertains to the stripping of fragile ground cover for the access road and rig location. Left alone, it would take many years for vegetation to grow back.
Identifying oil-bearing structures would require a series of single exploration wells at different locations; fields identified in this way could then bve exploited by drilling multiple directionsal wells from a single location. It is possible to use a heli-portable rig, which eliminates the need for the access road, but at significantly greater drilling cost.
For successful wells, some infrastructure would be needed, mainly a surface pump and either a connection to a trunk pipeline or truck-serviced stock tanks on location. A pipeline must be surface-mounted because of the permafrost layer, and must allow for migration of wildlife, as with the pipeline to existing North Slope fields. The average economical life of an oil or gas field is 25-30 years, so environmental effects could be expected for at least this amount of time.
Lastly, moving the crude to the lower 48 would involve increased shipping traffic. AFAIK, nearly all large spills have involved tanker accidents, so this would the mosty likely source of major, long-term environmental effects. Recently, there has been increased discussion of constructing a rail link between Alaska and British Columbia; while the potentil for spills would still exist, any worst-case rail accident would have considerably less impact than a tanker sinking.
None of these effects are ‘permanent’, and impact could be further minimized by specifying that only some small land area (say, 10% or less) of the wilderness lands could be altered by drilling production operations.
Hope this helps.