Dell actually has the right to go public if they want to. Is it the right thing to do? That's a different story entirely. It seems a bit greedy to some and against company ethics as well. But, they do have the right to do so. In fact, they are going public because it was just announced by a company representative.
Dell going public isn't such a bad thing, not even for its investors. They can now take part in a deeper investment strategy and can have the potential to make even more. Some will want to and will take advantage of investments such as the public trading of VMware where others wil not and will remain very unhappy about Dell going public. Like most things, it's a divided stand.
There is a difference in having the right to go public and the question of whether it is wise for Dell to do this. It's a matter of their return to public operating rather than private, which option they took in the 2010s when they transformed the company via acquisition and investment.
In 2016 Dell wanted to make sure the world knew of their move from hardware after acquisition of fellow tech giant EMC for $67 billion. EMC owns data storage, software, and security assets that are more relevant to the computer industry. The Dell company is probably in much better shape now and ready for the spotlight.