In absolute fairness to Toad, he is pretty heavily associated with power ups, and has been since Super Mario Bros. 3, where he was in charge of the item houses. Several power ups being mushrooms (like the Propeller Mushroom, for example, which also calls back to Toad's first platformer playable appearance since SMB2) also furthers the connections to Toad.
Back in the pre-Captain Toad days, the go-to Toad moveset plan as far as his specials was usually something along the lines of neutral special Ice Flower, up special Propeller Mushroom, side special Golden Mushroom (which, funny enough, would always work a lot like how Wonder Wing ended up working), and down special Vegetable Pluck that differed from Peach in terms of power and speed. The normals tended to be things like headbutts and spore attacks, and even summoning mushrooms like he does in Mario Sports Mix. Then there was always special emphasis placed on his throws, making him almost like a grappler.
Very similarly to how King K. Rool pretty much always had the same moveset idea in fan interpretations (save for down special, which varied), Toad was very similar in this regard. It wasn't until the rise of Captain Toad that it diverged from this a bit.
The 2011-2013 speculation period was a very different time.