As a general point, people who are willing and helpful are much preferred to those who are not so co-operative. For a manager, there's really no contest if it's a choice between trying to persuade a recalcitrant person to shoulder a task (with the strong possibility that if they are made to do it, they'll execute it poorly in order to avoid being asked again), and handing it to the person who has proved accommodating in the past.
So, on the face of it, your attitude is welcome to your manager, and your behaviour is in line with what is expected from high-performing people these days. But at the same time, there are dangers. You could find yourself overloaded with tasks that aren't really your responsibility and that will be difficult to execute well. These could stop you doing your own work to the standard expected. And often, the additional jobs you are assigned will be those that others don't want to tackle - because they are tedious or low-status within the organisation.
This makes your additional work less interesting and more stressful, and, over time, you may become exclusively associated with this kind of task - which may damage your chances of promotion to a more senior role involving more prestigious work.