That thought did cross my mind LOL
I was thinking the same thing
Archerm 3, are you a liscensed pilot?
My guestimates were for a C-150 flown solo, which I think of as a "typical" aircraft... If you like, here are some more refined numbers.
1/4 mile is 1320'.
From my copy of a 1973 C-150 owners manual(which only seats for 2 by the way):
1600 LB gross weight. No wind, Sea level at 89F would yield a takeoff run on grass to clear a 50' obstacle of 1673'(300' past mid field on a 1/2 mile runway). Under those conditions and at 1600LB gross, you would get about 635 FT/MIN of climb(corrected for 89F air temp) at 76 MPH best Rate Of Climb airspeed. A cessna climbing at 76 MPH covers 1.26 miles every 60 seconds. So for half a mile, that is about 250' of altitude gain, plus the 50' started at... Those are of course worst case hot and heavy numbers, and the published data in the manual for clearing a 50' obstacle is generous. cooler air temp, solo pilot numbrs for this aircraft are much better... That is also if the OP lived 1/4 mile right off the end of a 1/2 mile long runway. If the airplane was flying a pattern, he would of course be airborne longer and would have climbed to a greater altitude...
4 reasons to be motoring around at low level at full power, or making radical power adjustments repeatedly at low altitude in the vicinity of an airfield? I am curious, what are they? What have I missed, or forgotten over the years... Sorry, with my training and experiences, I really can't think of any reasonable excuse why a properly trained pilot would be doing so, except ag work or some sort of inflight emergency... Maybe once or twice due to errors or practice, but it is just not a good idea to be doing so on a regular basis. It is afterall his home field, he should know how to approach and land on it. Engines can and do quit. If you are repeatedly dragging your butt low over the trees with power to reach the runway, you are going to eventually get bit. Always leave yourself an out!
As for pattern distance, on downwind, I don't know about you, but I am used to looking down at the runway at about a 45 degree angle. At 1000' of elevation, that yields about a 1000' of horizontal separation from the runway. Unless my high school geometery teacher lied to me

Gotta stay close enough to land safely if the engine quits... For example, a C150 is only going to be able to realistically glide about a mile from an altitude of 1000', once the turn toward the runway is completed. That leaves no room(altitude) to linup and make a safe landing. 1 mile was a very poor guess... With the instructors I have flown with, flying a pattern that wide would be a good way to get beat upside the head with your knee board(while it was still attached to your knee

)
The OP's description of this pilots behavior, unless grossly overstated, does not sound like the actions of a prudent and safe general aviation/recreational pilot, at least none that I have ever known, flown or trained with.
You are most certainly right about the non pilot misjudging altitude...