If it does not violate electoral laws or how our constitutional Westminster style of government works then it it is all still legitimate. We also don’t use a coloured pine cone system either. It does not mean what we currently have is illegitimate because we don’t use another different system.It is electorally not legitimate because we do not use a popular vote system, so total popular vote is electorally irrelevant. As well, if political parties do not campaign on forming a coalition, then I submit they have lied to the public in order to gain power and the GG should not allow them to form a government. Doing that (and exactly what the NDP and Liberals have done) is a sneaky bait and switch on the electorate and should have forced everyone back to the polls to decide if that's what they want.
Parties are in no way beholden to promises they did not make. Promises made and elected on certainly give them mandates to do and effect their plans. How they decide to get the confidence of the house using the rules as written but sorely misunderstood by the electorate is not in question nor should it be. We have a system that says they can still attempt to form government if the party with the most seats cannot. Coalitions are not illegal nor are they forbidden.