They could easily build it in six years if they did a railway alignment, which would work better for the athletes' village anyways. They could either run it on the surface and then have it go underground as it approached Union, or dig it out via cut-and-cover. They wouldn't have to build the whole thing, even the Cherry to Exhibition chunk would be a huge asset. It wouldn't actually function as a relief line (that could come later), but it would greatly speed up transit between the village and the Skydome/Exhibition where so many of the events are going to be held, and by connecting with Union it would make it far easier for athletes to get everywhere else in the city.
In no recent games, be those Olympic or Pan-Am or otherwise, have the athletes taken public transit. They're moved by private automobile.
As far as conventional wisdom in planning multi-sport games goes, you want the athletes/coaches/officials/etc. as isolated from the general public as possible. Facilities and transportation planning are built around the idea of moving VIPs from a secure compound (euphemistically, an athlete's "village") point-to-point via a single isolated mode of transport to a special entrance at a sporting facility, and back again.
Why? Well, there's the Munich '72 legacy in terms of security, for one, which has undeniably shaped planning for all subsequent Olympics and then sort of trickled down to make that style of doing things de rigeur for all largeish multi-sport games, be it the Francophonie Games or the Junior Goodwill Games or what have you.
But even leaving security reasons aside, organizing committees have a bit of fetish about control. The less interaction with externalities beyond the organizers' control (the subway breaks down, local farmers protest land-use policy at the legislature, a police investigation closes an intersection, an athlete wanders off to The Brass Rail and misses their qualifying heat, etc. etc.), the fewer possible things that can go wrong. That's the main reason nobody envisions athletes hopping on a train with the general public these days. It's not because there's a substantial risk of one of them getting knifed. It's because it adds variables to an already-complex equation that millions of dollars are riding on coming out exactly right.
Now, I absolutely agree that this kind of bunkered private-vehicles-first thinking would be a lousy way to build and run a real city, but ultimately all the organizing committees are concerned about are the two weeks the games are on. A fleet of minivans and several thousand meters of metal fencing along roads meet their needs more than adequately.
Frankly, I'm glad we're not laying out transit on the basis of passenger flows for a one-time event that lasts two weeks. If we were looking purely at transit through the prism of the Pan-Am Games, there'd be absolutely zero incentive to spend a penny on the Eglinton route (be that on a subway or a streetcar or hypersonic vacuum-tube train) as there will be next to zero athlete or spectator traffic in that neck of the woods.