Rather than removing an automobile lane, couldn't they just build/install a bike lane parallel to Parkside on the High Park side?
Probably. It would be fairly expensive because there's a lot of sloping right next to the road in parts. And you'd have to cut down a lot of trees.
The answer is "No" they could not.
Its not simply a matter of cutting down trees, though certainly, that would be an issue.
This is Parkside just south of Bloor:
Beyond hat guardrail the land immediately slopes downwards at a steep angle.
The land between guardrail and the curb is of insufficient width for a Cycle Track here, but even if it were wide enough, you've have to relocate the streetlights and the power lines. The lines can be buried, at considerable cost, but where would the streetlights go, you'd have to cut down trees on a slope, within a park, (not generally permitted, but that aside, you would create slope stability issues (the roots are holding the ground in place, which is also the road bed) .
The level ground widens out a bit to the south, but then you encounter more problems at Indian Valley Road.
Looking north from that intersection:
Note the grade change, the narrowness, slopes above and below, as well as a retaining wall.
But then, cast your gaze south:
Once again, you find the space between the guardrail and the curb is not sufficiently wide for a bidirectional multi-use path or cycle track, and there is again a steep fall off here. Ecological damage aside, removing trees of the size you see here is a 7-figure cost given the site area and conditions, and that doesn't account for the infilling and re-grading the slope, which would require an Environmental Assessment and 7 or more likely 8 figure budget.
Then we can look south of High Park Blvd (streetcar loop):
Here, again, you have severe constraints which would require the removal of the retaining wall, most or all vegetation above same, a new retaining wall, much taller, would be cut in mid-slope........... the budget for this idea isn't high, its increasingly stratospheric.
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To be clear, the idea of putting in an MUP/bi-directional cycle track next to the park, beyond the existing curb, would be a non-starter politically, from a regulatory perspective and fiscally.