We have a bunch of former rail lines converted into trails. The Belt Line trail is a famous one and there's also the Leaside Spur Trail in Don Mills.
If you're going to ask "why don't we have rail bridges converted into trails" you first need to ask if we have many bridges to begin, and if any of those aren't being used for trains. Hint: We don't. There's the one discussed in this thread and the old radial line bridge that crosses the Humber (and has been converted to a path), but that's pretty much it. It seems like a foolish question to begin with, like asking "Why don't we have any great Ski resorts? I lived in Whistler and can't see why we don't have that here."
The reason why the Belleville Sub bridge over the Don hasn't been repurposed is because there's plans to re-use it for trains one day. Any trains that come from the CP lines to the northeast (from locations such as Malvern, Peterborough, and north Pickering) would need to use this line to access Union Station. The line and bridge is owned by GO and plans for putting it back into service are discussed on a regular basis.