I have no idea if this is true, but I remember seeing in a Kurzgesagt video that developing phage resistance reduces antibiotic resistance, and vice versa. So you might corner bacteria by using both.
Improving phages is dramatically easier - you can just modify an existing one, either through direct engineering or by evolution, rather than having to find a brand new chemical that conveniently does what you want without serious negative drawbacks. 20 years ago the difficulty may have been comparable but the engineering tools for creating synthetic phages have advanced extremely rapidly.
And particularly if you are introducing a vulnerability instead of directly attacking the bacteria with the phage, there is no evolutionary pressure to become resistant until the phage has already done its job. You can even go further and have it insert genes that confer an advantage in addition to the susceptibility, so that even if some of the bacteria are by chance naturally resistant to the phage they get outcompeted prior to the deployment of the killing agent.
https://www.youtube.com/watch?v=YI3tsmFsrOg&t=5m18s