Quite appropriately, the
one major office building constructed downtown in the 1920s was built to house the headquarters of the provincial wheat pools, and later became the HQ of the Canadian Wheat Board. The changes in Canada's grain economy had far more of an impact on Winnipeg than the Panama Canal.
Add to this the effects of the Great War and recessions that kept away the British investment that paid for so much of the pre-war building in Winnipeg... in addition to the worldwide notoriety and local shock of the general strike... the old elites fading away, and the new generation of elites being comprised increasingly by branch managers rather than owners...
Not that Winnipeg didn't experience growth in the 1920s... the population increased by 22% in that decade, and an incredible amount of construction occurred throughout the city, particularly many new walk-up apartment buildings in older neighbourhoods, smaller commercial buildings on what are now the old main streets, and whole neighbourhoods built up. It's just a little conspicuous there's no gleaming art deco/gothic-inspired tower as a result.
It would be hard to substantiate a widespread belief against tall office buildings in Winnipeg (or Canada generally) before the 1960s or so, but I think there's something to what Andy6 says. Even during the boom era, in 1907, a proposal to build a 14-storey building on Main Street was opposed by the City's Board of Control and Mayor Ashdown, the latter of whom felt that there was no reason for buildings to reach higher than the Merchant's Bank (seven stories). Funny enough, this was the site where the wheat pool building went 20 years later.
Still, I don't think this aversion to skyscrapers was unique to Winnipeg among Canadian cities, or is a significant reason why Winnipeg didn't see tall buildings in the '20s. Even the stridently British Canadian cities like Toronto built the Sterling Tower and the Royal York.