The C.D. Howe Institute (hereafter CDHI) presumes that it can measure academic benefit. I have no idea how they did, not having the study at hand, but let's grant this presumption. CDHI also presumes it can non-controversially delineate a lower-class (or lower-income) family -- again, let's grant it. Finally, let's grant the result: that lower-class and single-parent children benefit more academically.
This brings us to the heart of the problem I have with the conclusion: that there's no negative side-effect of isolating lower-income and single-parented children from their more well-off peers.
Here's one negative side-effect: it screws the middle class over. Part of the childcare problem in Canada, insofar as I understand the issue, is that there aren't enough spaces to go around. Thus, if the lower classes are being subsidized, and the upper classes can win in a head-to-head market-based competition, the middle classes get frozen out.
Here's another negative side-effect: if we're trying to create a diverse, but integrated, society (and surely that's the aim?), we shouldn't be imposing more artificial barriers between people of different backgrounds. Hence, we should allow for children from different backgrounds to interact with each other, at least in the limited amount of time they will spend in childcare, in order to, as much as is reasonably possible, break down any inherited prejudices and bigoted attitudes. (This will also, incidentally, probably help the families of the children interact with each other as well.) Of course, unless there's actually a ban on privately-provided childcare, like there is on physicians accepting private money for providing OHIP- (or equivalent-) covered services, the upper classes will still probably opt out. At least, though, we could get a little lower class/middle class solidarity going, which is no bad thing.