Is it just as bad if Trudeau wins a majority with a mandate from just 30% of Canadians?
Yes and no. From the POV of true participatory democracy, yes, just as bad. From the POV of "representing the views of a true majority of Canadians", it would be an improvement. Kind of like getting a better outcome but for the wrong reasons.
Depending on how the polls questions are phrased and when the polls are taken, results fairly consistently show that about 60-70% of Canadians identify with left or centre-left values. If we had a real, functional proportional electoral system then we would probably see few, if any, majority governments being formed, and coalition governments becoming the new norm. Most likely this would mean Liberals leading, with NDP and/or Green participating in the coalition. Cons would fade into being either offical opposition or the third party. In a 338-seat parliament, a well-executed proportional voting system would yield;
Lib - 118 seats
Con - 110
NDP - 68
Grn - 24
Blc - 14
Oth - 4
An easy win for a Lib/NDP coalition that would be truly representative of Canadian values. However, I think that a proportional voting system will change the way Canadians vote. I would be tempted to vote Green if I like the candidate and I knew my vote would really count, and I suspect many others would also. If the system were something like STV, a lot of Cons might put a Lib or Indy candidate as their second choice, so when the Con gets eliminated in the first round, it would boost votes for those other candidates.
We really really really really need a complete overhaul of our electoral system FPTP is a dead horse.
When one person suffers from a delusion, it is called insanity.
When many people suffer from a delusion, it is called religion.