Back in 2006, when I had a broken leg and had to use crutches, I greatly appreciated the electric grocery vehicles. Shopping would have been much more difficult without them. However, I put it away properly after unloading it into my car; I even plugged it in. The only (temporary) proof I had of being (temporarily) handicapped was the card that enabled me to use handicapped parking places. I didn't use it if regular parking places were reasonably close.
It's certainly true that some people have become disabled because of obesity. Their extreme weight damages their joints and their damaged joints cannot support their weight.
Yours was the appropriate use of this assistive equipment that I expect to see. And I realize that obesity can cause genuine & disabling joint problems (although in most cases I think they would come under the heading of what we unsympathetically termed in the Army a "self-inflicted wound").
But if there is genuine joint damage causing limited mobility, as I have due to arthritis and injuries, then that is easily established medically and officially by the State. As you appropriately did when you got a temporary (red?) car parking permit during your convalescence.
BTW, we sometimes don't use our handicapped permits, either (we each have our own). But it's more because a non-handicapped open space is occasionally closer to where we need to go than the handicapped. The placement of marked handicapped parking spaces is often inconsistent and illogical, and not always the most convenient.
One nice feature of handicapped permits in most of Florida, however, is that they negate the need to pay into public parking meters, when not parking in a handicapped space (which are all unmetered). Your parking becomes free. And in some places like Key West they override their 12-hour maximum use local rule for a space - you can park in place continuously for days, which we've done.
Another thing: while some days we feel "chipper" when we arrive, and could easily walk from farther away, we can't be sure we'll feel that way when we leave a place some time later. My joints can start howling without warning. And if we're carrying stuff on the way out, even pushing a heavy cart, we really need to be closer to the exit. So we do get good and appropriate use from our permits.