That might be a good idea but it has nothing to do with the slow start on the cord. When you first started it it had no air therefore no load on the pump on start up when the electrical draw is the most.
If the switch was set to come back on at 100 lbs the pump had that much load to overcome and demanded even more current which wasn't there in sufficient voltage to get the motor off the start circuit. You can easily burn up a motor that way.
If you get a 50 ext cord that is 12 ga. it might work. Most don't buy those because they are 3x the money.
The heavier duty the cord the more $$ it will cost. Most people won't buy them you are exactly right, but they'll spend $1000 on an air compressor or other high amp draw device and keep burning them up

. I did finish carpentry for a while, most of the guys had junk HF direct drive oil-free air compressors. Every few months they were having to buy another one. Not just because of the junk HF compressor actually they weren't too bad, it was they would burn the motors up because they were using 18-16 gauge extension cords plugged into triple tap extension cords that were already overloaded at the jobsite. My 30+ year old Montgomery Wards 1hp/10 gal air compressor is still 100% original, I do need to replace its power cord here pretty soon as the sheathing I noticed is starting to come apart. However, I've hardly used it with an extension cord, and if it is I have a 12 gauge extension cord that I plug it into on that rare occasion. I usually just hook up another length of hose which is what I did when I was installing the new base boards in the house last week. Just 2 50' hoses got the job done, and the compressor stayed outside.
If you are doing a lot of air tool use using tools that require lots of CFM, you'll want that compressor tied to an outlet, or a very expensive heavy duty extension cord or you'll be tripping breakers, and/or starting electrical fires. Possibly even burn the motor up in the air compressor as well due to the under-voltage/amp problem using a cord that's too small. My compressor will kick a 15amp breaker when the temps are really cold, once it runs a cycle though it would be fine, but I try and keep it on its own circuit whenever I can as well. That can cause issues if you try and run that compressor on a shared circuit, that may cause slow startup, where the motor doesn't come to full speed, which means it never switches from the starting circuit to the running circuit, it quickly overheats the windings and burns up the motor.