The reason its #1 in most of the country is because those provinces mutually agreed to have it be #1 (and #16 for the Yellowhead Highway). Highway 1 in BC is technically British Columbia Highway 1, they just have their own logo for that route specifically (that just happens to match the logo in Alberta, Saskatchewan, and Manitoba). However for many of the provinces, doing so would completely break how their highway system is numbered. You could rename Highway 17 to Highway 1, but what do you do with the 417? I don't think Ontario wants to downgrade a 400 series highway to just a regular highway and break their naming consistency even more just to have a consistent Highway 1, and in Quebec/Nova Scotia this is even more of a problem since they have an even more consistent and organized highway system. In Quebec they have odd numbered highways for north south routes, even highways for east west routes, and the highways go up in number as you go north, and east respectively. Breaking all of that just to have a highway that jumps from highway to highway (the main TCH route goes through 4 different highways as well as a provincial road from end to end in Quebec) would just be silly.
Nova Scotia has a similar setup to Ontario where all of the arterial routes are "100 series" and the number corresponds to the trunk route that typically runs parallel to it (so the 104 runs next to Highway 4, the 102 runs next to Highway 2, and etc. Not only would Nova Scotia have to reorganize its highways, but they would also have to change how the arterial-trunk relationship works since best case scenerio, the 104 will be renamed to the 101 and not the one. This also doesn't mention how on Cape Breton, the main TCH route jumps from the 104 to the 105 so you still have that to worry about.
Finally an inverse case. Prince Edward Island has a TCH branch running through it labelled as "PEI-1", and is named as such because its the main highway running through most of the province. However as a branch, it connects to NB Highway 16, and NS Highway 106 respectively, which are branches off of the main TCH route. Should PEI 1 be renumbered to something else since its a different TCH branch altogether?