I have tended to keep the choke open a while, closing it progressively as I have found that if I close the choke "too soon", the car idles at progressively lower revs and then stops.
This is normal operation. When the carb is adjusted right, I would expect to need to use full choke for a cold start, then after 15-30 seconds you can bring the choke down to around half and you can start driving. Letting a car idle up to temp is not the best way to warm it up (unless we're talking about pre-war cars using splash lubrication and single weight oils).
After a mile or two you can turn the choke off. This will con-inside with hints of warmth coming through the heater, suggesting the engine is getting warm. If you turn it off a bit soon you'll feel the engine just feels a bit flat.
Black plugs do show a rich condition, but if you've only been doing short diagnostic drives, not getting off the choke much, or if the plugs simply haven't been cleaned for a long long time, then it can be a red herring.
When the car starts to loose power, if you pull over and let it idle for a minute or two, does it pick back up and run ok for another mile or two? If it did, that would be indicative of a fuel supply issue, where a weak pump or partially blocked lines/tank do not allow enough fuel flow to keep the carb topped up when working the engine hard, but when the engine is only sipping the fuel at idle then the carb can refill.
If it doesn't then I would suggest checking the quality of the spark once the engine is showing the problems. Some coils when beginning to fail can show up problem when hot only.
I would also suggest checking the valve clearances. If they have closed up, which is not unheard of in these engines, then you might find that the valves are starting to be held open as the engine warms up and the loss of compression is causing the loss of power.