No, it isn’t mandatory and you can request for an Australian visa in different ways. Although if the work experience that you claim to have isn’t aligned to your educational degrees, it could pull you back a few steps. For instance, you may be an Arts Major, but working in IT (Information Technology). In this scenario, it is the Australian Computer Society (ACS), which will assess your work experience and also take into consideration your educational background. But the latter is in Arts domain and so the ACS will deduct a chunk of your work experience for this very reason. You just might have to submit an RPL (Recognition of Prior Learning) application in this case.
Moreover, the visa process is all document based and to explain and clarify a mismatch between your degree and work experience is again time-consuming and document heavy. Having a degree in the domain of your work also helps to accumulate higher immigration points, which assist you in receiving the ITA (Invitation to Apply) quickly.
Since you ask about the significance of your work experience in this process, let me tell you that it is a very important one, just like the factors of age, skills, educational qualifications, language ability and the likes. And, just to be eligible to apply for an Australian visa, you need to score a 60 on 100 in the point’s grid.
Anyways you are offering a huge fee to the Australian government while submitting the visa application and are also getting 2 years from your work experience deducted in the name of training years, so make the other years count. The more they are aligned to your degree, the better your chances to reach the 60/100 score for that ITA.