Tag Manager is undoubtedly the future of conversion tracking. The old days where you put a tag for analytics on every page, had another tag for remarketing lists and a tag for each conversion on Adwords among other tags such as facebook etc is gone. No longer do you have to contact the developer for every new or changed tag which was time consuming and ineffective. Tag manager allows you to place one tag on each page of the website and then manage all subsequent tags from a centralised location with debugging features and multiple user access.
If you're not tracking it, you cant improve it. Thats why tag manager is so important. It allows you to save time, money and effort on getting all your conversion tracking and remarketing tags set up without any co-operation from a developer. It is also much more effective than having the individual tags that were prone to error and slowed down loading times. Tag manager loads asynchronously leading to improvements in loading times and accuracy.