The Constitution likely does not permit Parliament to restrict the prerogatives of the Governor General to dissolve the House on the advice of the PM. Had the legislation sought to prevent the Governor General to dissolve the House, the legislation would likely have been unconstitutional and hence been even less effective than the actual legislation was.
To move to a true "fixed date election" model, we would have to abandon the "responsible government" model whereby the government holds office at the pleasure of Parliament and allow the government to remain in office in spite of Parliamentary opposition. This would require constitutional amendment.
While Parliament is competent to unilaterally amend the constitution "in relation to the executive government of Canada or the Senate and House of Commons" (section 44), amendments regarding "the office of the Queen, the Governor General and the Lieutenant Governor of a province" require the unanimous consent of both houses of Parliament and the legislative assembly of each Province (section 41(a)). As the dissolution of the House is historically and traditionally a prerogative of the crown, exercised through the Governor General, removing this prerogative would likely fall within the ambit of section 41(a) and require unanimous consent of the Provinces.
Keep in mind also that the Conservatives did not have a majority at the time of the adoption of the so-called fixed date election amendment. It was adopted with the consent of opposition MPs as well.
To move to a true "fixed date election" model, we would have to abandon the "responsible government" model whereby the government holds office at the pleasure of Parliament and allow the government to remain in office in spite of Parliamentary opposition. This would require constitutional amendment.
While Parliament is competent to unilaterally amend the constitution "in relation to the executive government of Canada or the Senate and House of Commons" (section 44), amendments regarding "the office of the Queen, the Governor General and the Lieutenant Governor of a province" require the unanimous consent of both houses of Parliament and the legislative assembly of each Province (section 41(a)). As the dissolution of the House is historically and traditionally a prerogative of the crown, exercised through the Governor General, removing this prerogative would likely fall within the ambit of section 41(a) and require unanimous consent of the Provinces.
Keep in mind also that the Conservatives did not have a majority at the time of the adoption of the so-called fixed date election amendment. It was adopted with the consent of opposition MPs as well.

