(tl;dr? Skip to the last three paragraphs.)
The reputation cap is one of the network's longest-running features, having been set at 200 since the month Stack Overflow launched, if not earlier. Records from back then are... spotty.
Many features we take for granted today, like restricted editing, review queues, and association bonuses, didn't exist when the site was born. (On the other hand, closing was much crazier, with only one person needed to shut something down, so there is something to Glorfindel's answer.) Based on vague memories of the early days, observations of how the team operates, and general background, I'd say the rep cap made it into the system so early for two reasons:
People are naturally going to think a lot about reputation scores. The underlying "game" of the site is designed to take advantage of that, for Pete's sake. But not everyone is going to be able to rack up massive scores, even if they're equally capable. Those pesky "jobs" and "real lives" get in the way. Having a cap reduces the amount to which simply spending time on the site correlates to rep, which ultimately helps maintain reputation's purpose as a coarse-grained measure of trust (both "how much trust should you put in this person's content" and "how much the system and community trust this person to behave").
I'm pretty sure I've seen something from Jeff Atwood about this, but I can't find it now. Instead, I'll quote cletus (source):
It acts as a hint to limit yourself to a certain amount of time on the site each day. Of course you can stay as long as you like but the daily cap is a gentle hint that maybe you should be doing something else for awhile.
This might be annoying in the short term, but keeps users coming back and being productive in the long run instead of getting addicted and burning out.
The rep cap is a failsafe against users gaining a boatload of reputation off of a single post that gets wildly popular for just a few hours/days. This, too, was more of an issue when the site was nascent, when more discussion-based, opinionated, and/or humorous posts (not to mention bug reports and feature requests) were permitted on the main site.
To tie this all in with the actual magnitude question you asked... I again can't say for sure. I spent a lot of time trying to find the actual origin of the rep cap, and couldn't. The farthest I got is finding out that it originated as a UserVoice request back when Stack Overflow was in beta. For reference, see Bernard Dy's comment on Aug. 25, 2008 at UserVoice post fix this limit for voting, or a brief mention Jeff made in Podcast 019, which was released the following day:
we're currently recalibrating a bunch of things and I think we're about to piss off a bunch of our audience 'cos we're going to put in a whole bunch of reputation caps which they're not going to like!
One thing I do know is that many early site decisions (and, for that matter, some more recent ones) were made by gut feel. I strongly suspect that someone simply picked 200 as a number that felt not-too-high and not-too-low, and then when it seemed like things were going well, the value stuck.
This could be attributed to both the "if it ain't broken, don't fix it" factor, and users getting anchored to the starting value, such that any attempts to change it would have probably met with unhappiness. And it does seem like a nice middle ground, where you can get a few decently upvoted posts up in a day without "losing out" but not be encouraged to be reading SO 24/7.
One last bit of speculation: the cap was actually part of a response to complaints about the previous reputation control system (limiting people to just five or six votes per day), so it's possible that rep-related numbers from that era were factored in, at least qualitatively.