Mary Tudor OTL and ITTL is not yet married with Louis XII and is still betrothed with Charles of Habsburg (alias Catherine nephew and future Emperor Charles V) and I do no think who the Royal Council would like neither having England added to the Habsburg domains or a young female unmarried ruler free to choice herself her husband, specially not when she has an older, just widowed older sister, who is both the lawful and rightful heiress and the regent of Scotland and mother of their young king. Margaret is an easier choice than Mary because she is widowed with two small sons (thus male heirs who can carry the line and make her mother a much less rich prize) and can put all the Scotland under English control definitively.
Margaret is a Queen who they can control and any new husband of hers will not have the same control who an husband of Mary can demand.
With Mary Tudor as new Queen they: first denied the Crown to the legitimate heiress and endangered more the English/Scottish relationships, second put the England in Charles V hands or on the matrimonial market with the risk who Mary decide, being her engagement broken, who she is the Queen and can marry whoever she want and make a very bad choice of husband (and remember who OTL Mary, just widowed remarry almost immediately with Charles Brandon). If James IV would be still alive maybe the Privy can have a good reason for denied Margaret the Crown but with the enemy dead better take Margaret and her boys of impeccable royal blood and put the Scotland under English control ending the danger of other Scottish invasion instead of giving them a very good one for future wars (because if also Margaret decide to marry some unsuitable man the Privy can denied him powers more easily or denied the control of England to a foreign husband with the excuse of Margaret's boys)
Margaret is a Queen who they can control and any new husband of hers will not have the same control who an husband of Mary can demand.
With Mary Tudor as new Queen they: first denied the Crown to the legitimate heiress and endangered more the English/Scottish relationships, second put the England in Charles V hands or on the matrimonial market with the risk who Mary decide, being her engagement broken, who she is the Queen and can marry whoever she want and make a very bad choice of husband (and remember who OTL Mary, just widowed remarry almost immediately with Charles Brandon). If James IV would be still alive maybe the Privy can have a good reason for denied Margaret the Crown but with the enemy dead better take Margaret and her boys of impeccable royal blood and put the Scotland under English control ending the danger of other Scottish invasion instead of giving them a very good one for future wars (because if also Margaret decide to marry some unsuitable man the Privy can denied him powers more easily or denied the control of England to a foreign husband with the excuse of Margaret's boys)