Wrong. It cost him his Prime Ministership.

Abbott was dumped and Turnbull, who never shied away from his support for Same Gender Marriage = Equality said he would honour Abbott’s promise.
Yes, it may have been a very expensive exercise.
Yes, and in this the loud mouths within the GLTBIQ Community were in lock-step with the Australian Christian Lobby, opposed it.
BUT
If Turnbull had not gone ahead with it we would still not have the same Rights as the rest of Australian Society. Turnbull did not have to respond to the result. He could have done what Tony Abbott would have done and simply ignored it.
I am not sure what the rules are but I suspect as PM Malcolm Turnbull could not have introduced his own Private Member’s Bill to change the Marriage Act.

No Liberal Prime Minister can order any of his MPs & Senators to support an issue to which they are strongly opposed if it is in conflict with their what passes in their minds for moral beliefs.

The ALP is different. If you speak against or vote against ALP policy you are automatically expelled from it.

If that Plebiscite had not been held and the issue had been put to the Federal Parliament – the only place the Marriage Act can be changed – it would in all probability have been defeated. Don’t forget for the ALP, the Nationals and Liberals their Party Policies were Opposed to Same Gender Marriage. Yes, Liberals can cross the floor and vote against Liberal Party Policy (so long as you are not in the Cabinet. ALP MPs & Senators don’t have that Right. They must vote in favour of ALP Policy.

What did you want? The Right to marry the person you love or to remain a Second Class Citizen?

Turnbull can’t stop anyone from saying what they think. Imagine the outcry if any PM managed to change the Law so that he/she could silence any of us.
That is the sort of thing Hitler, Mussolini, Stalin and Mao did (and the current Chinese Communist Dictatorship still do)
All these claims – and yes I saw some of the dramatics on TV – were just that drama for the sake of drama.
Turnbull made it possible and it is one of the reasons some within the Coalition – Tony Abbott, Kevin Andrews, Peter Dutton, Erich Abetz (have a look at Erich’s family history) turned on Turnbull and we have now lost one of the Fairest, Most Decent Prime Ministers Australia has ever had.