But, I now understand the problem. At my organisation we have only 2 DBAs, and we can't give all of our time to this task.
To be a DBA is an endless battle against the entropy some devs try to create. The data model should really always be validated by someone with more knowledge and experience. Also, some young devs come up with crazy ideas (for instance, we should not use foreign keys). Others want to load insane amounts of data to process in the database, instead of preprocessing, or using a staging database. There is a continuous stream of bad ideas being implemented.
And when a bad idea gets implemented, it is really hard to undo it and it tends to just create more chaos: you need materialised views to get around bad modelling, or weird views to compensate for duplicate data, etc.
So, yes, a DBA is a really important role. With regards to it being a good job, it depends if your company takes it seriously and puts you in the development process, otherwise you'll be in for a lot of stress.