So how do commercial/industrial lab supplies have a 1A output that supports 100k loads?
I would be really interested to see such a supply...
And do they always generate such high voltages or does it ramp up until the expected current is met?
As you already discovered yourself: there's no way around Ohm's Laws. The implication of that law (V = I * R) is that V and I can never be independent from eachother.
A laboratory PSU with adjustable voltage and current will work in CV (Constant Voltage) mode as long as the load does not exceed the set current limit. When that limit is reached will the mode become CC (Constant Current).
In a sense such a lab PSU is not a current source, rather a voltage source with adjustable current limit. A lab supply will simply switch to CC mode once the current limit is reached and while the load is increased even further, the voltage will drop until the load is a short circuit. Going the other way, it will go into CV mode again.
In my work I test measurement instruments used for EIS (Electrochemical Impedance Spectroscopy). These are called Potentiostat/Galvanostat, or short PGStat.
In PStat mode it functions as a voltage source, in GStat mode in functions as a current source. Basically CV and CC.
Now this is a true current source (in GStat mode) as it will keep the current constant regardless of the load that is connected until the voltage limit is reached (compliance voltage).
So e.g. a 20 V/200 mA PGstat could supply e.g. 10 mA into a load in the range from 0 Ohms to 2 kOhms. At 3 kOhms, you would need 30 V to reach 10 mA, which it can't.
At 1 mA, the range would be 0 to 20 kOhms. And at 100 mA it would be 0 to 200 Ohms.
So now you will probably understand why trying to supply 1 A into a 100 kOhm load is a very tall order.
Actually, PGStats can also sink currents, but that not relevant for this topic.