You're going to get a lot of "2 cents worth" comments on this. Although a fast idle of 2000 rpms sounds a little high, I don't think a static fast idle is considered damaging to a cold engine. Not sure but I suspect most EFI fast idle programs are for building up catalyst heat quickly, promoting a clean burn and minimizing emissions on start up cycle.
For my two cents a static fast idle (1500 - 1600 rpm) on a carbureted engine is fine to keep the engine running reasonably clean on a rich choke setting until the intake and carb warm up enough to promote good fuel dispersion and permit a reasonably decent idle. You don't want it chugging along at slow idle, unable to burn the rich fuel/air mixture and fouling the cylinder walls, rings and
oil with excess fuel. But as soon as it will pretty cleanly fire the cylinders then gentle driving and cycling the engine without gunning it or lugging it will help get all the mechanical bits warmed up quicker, keep the
oil moving and allow tolerances to reach their normal range.
I would be more concerned about gunning and reving a cold engine up and down in an attempt to get it to warm up enough to hold an idle. That's why I have a functioning choke and fast idle on all of my old cars - because I don't like having to sit there and constantly feed throttle to the engine and try to keep it running on a lean mixture while it's cold. But most of these cars are kept in fairly warm garages and a choke is probably not a real necessity on them. My thinking is that most of the wear on a cold engine is from actually starting it while it's trying to get the
oil circulating. For that reason I usually prime the carb on my engines if they haven't been run in a few days so that they fire and run on the first turn of the starter. I don't like the idea of sitting there grinding on the starter for a long period with marginal oil movement and pressure while trying to get fuel to the carb.
But there will be other theories I'm sure.