Historically, the highway numbers in were more integrated than they are today largely due to the divergent numbering schemes as the respective provinces started building freeways. Highway 2 existed from Windsor to Halifax, passing through Toronto, Montreal, Quebec City, Fredericton, and Saint John. While remnants of the original routing remain, if it followed present-day freeways it would follow ON 401, A-20, A-85, TCH 2 (NB), TCH 104 (NS), and NS 102. At the same time, the original QC 17 extended from ON 17 to downtown Montreal. As upgrades occurred, the respective provinces did the following:
- Ontario and Nova Scotia kept their original numbering system in tact and added 3-di on their expressways - 400-series in Ontario and 100-series in Nova Scotia. Ontario initially numbered their 400-series sequentially (i.e. 400, 401, 402, etc.) before moving to adopting the route that it replaced (i.e. 416, 417); Nova Scotia follows the route it replaced. Maybe Hwy 401 should have been initially designated as Hwy 402.
- Quebec totally renumbered their highways in the 1960s to its present system. All 2-di highways that were not freeways became 3-di on a grid.
- New Brunswick moved designations to the upgraded routes, with bypassed sections becoming 3-di.
And the TCH isn't even really taken seriously in Ontario in Quebec. They're just tacked onto existing provincial freeways and they are NOT posted at junctions (in Ontario at least).
I'd say that the reason we don't have US Routes or Interstate equivalents is simply because of geography.
Canada's population is heavily concentrated on the southern border so the population is more wide than tall. Also, population is concentrated instead of being relatively spread out across the country. Thus, it's not really that beneficial to have a national system and provincial systems do just fine.
There's only one major road that crosses the Ontario-Manitoba border, so that just tells you how unevenly distributed the population is.
They're not taken seriously in ON and QC but they are much more outside there.
With exception of the Ottawa area, the Trans-Canada Highway passes through Ontario's hinterland, so it's no surprise. If a branch of the TCH followed the ON 2/ON 401 corridor, it might have been taking more seriously. Land area aside, the reality is that over half of Canada's population lives in the Windsor-Quebec City Corridor and over 60% are in Quebec and Ontario - what's important to them is what ends up being important to Canada.