Or is there some other reason that it would be beneficial to invest on a daily basis that I am missing?
While I do like dollar cost average reason, despite what you say, which has it's merit too. The other real reason is the power of "everyday." Or in this case, every week. You're not going to notice it if it's going out in small little chunks, but it's going to add up to a huge amount. It's hedonic adaptation. You'll just adjust to not having that money. Now you can make the same argument to your side of the case, where you're still not going to miss it even if you do it right away in large sums, because, again, you'll adjust. However, if you're going to invest 400 in a month; you could do it on the first of the month, and see your account drop 400 right away, or do it 100 every week, and see it change slowly... I think at the end of the day, it's just a personal preference. I think that you should do whatever works for you psychologically.
Now, I'd like to see the math worked out. What the difference would be by doing everything on the 1st of the month, vs spread out over the month. Though that'd never actually show real numbers, because the proponents of dollar cost averaging would just be able to point out that the math would be assuming constant growth, where you could essentially buy high for that month, or low, when doing lump sum. Which again is why I think it probably just boils down to whatever psychologically keeps you investing.