I think it's a carryover from the days of film, when Canon always seemed to err a little on the side of underexposure, which helped protect highlights in slide film from blowing out.
However with digital there is more "headroom" with the highlights (a highlight is a preponderance of data in digital, where it was clear film or "no data" in slides)... In this respect, digital is more like negative film. (But digital's dynamic range is more like slide film than negs.)
The reason to set a little + EC much of the time is simply that it's safer to err toward slight overexposure now with DSLRs, better to have to reduce exposure in post... Than it is to underexpose and have to increase exposure in post, which always increases image noise disproportionately. So underexposure is the last thing you want, whenever it can be avoided.
Using a pre-set level of EC is really sort of like putting a one-size-fits-all bandaid on the auto exposure process. Ideally you should be dialing in different amount of EC for each and every image, but that's simply not practical much of the time. Plus, just how much EC is needed is likely to vary from one model with one type of metering system to another with a different metering system,m though many people think it's "safe" to give Canon cameras in general 1/3 to 2/3 stop + EC.
There's also some subjectivity with exposure. What I like might be different from what you like. Or what works for one subject might be quite wrong for another subject.
I do a lot of equestrian photography and, when using any AE mode and time allows, I dial in a little more + EC for a white horse (as much as +1 or +1-1/3) and a little less for a really dark or black horse (-1/3 to +1/3)... In the middle tonality bays, roans, grays and most multicolored I tend to shoot with about +2/3 EC most of the time.
Works pretty well, much of the time. This is one of those "Yeah! Nailed it!" moments...

A very dark chestnut horse in this case, but with a lot of "natural fill light" from the very reflective sand in this particular arena, I dialed back to +1/3. If there had been less of the fill light, I'd have dialed it back to 0 or possibly even -1/3 EC. 7D with the 63 zone iFCL metering system handle backlight like this quite well in Evaluative metering mode (using a single focus point, so the meter puts the emphasis on that), so long as the subject is filling a lot of the frame. Other older Canon models I've used a lot, with their 35 zone metering systems, weren't as good with backlit subjects.
A 1Ds Mark I uses an older metering system (probably similar to my EOS-3 film cameras), and if the camera hasn't been serviced lately might be a bit out of calibration in several possible ways. So you almost have to run your own tests with it to see what works for you. In your case, I might only use +1/3 as a starting point, take some test shots, then tweak the settings up or down a bit if needed. The testing doesn't need to be fancy... In fact if you are finding most of your shots are needing +1/3 or +2/3 in post processing, that's a good guide right there what you need to set.
You probably already know, but just keep in mind that this only applies when using the auto exposure modes (Av, Tv, P)... And not to M mode exposures (or longer B exposures, where in both cases EC isn't available anyway). If setting exposure manually (either by eye or with a separate meter) you are effectively eliminating the reflective metering errors or biases that are the whole reason for EC.