Well first of all we have to make it clear that we are talking about government debt held by central banks. Non-trivial amount of government debt will be borrowing from households firms and other governments where it is not valid to argue that the debt is an illusion.
When it comes to debt held by central banks not much would change although it would make reducing amount of money in circulation bit difficult for a central bank. An advantage of creating new money by purchasing government bonds is that the money can be easily destroyed just by central bank asking for government to pay back the money. In principle government has other options of how to reduce money supply even in such case but doing it through repaying bonds is the most direct way how central bank can do it without help of rest of the government.
This brings me to the final reason why such institutional arrangement is justifiable in the first place. It is virtually agreed by most economists that central banks work best when they are independent technocratic institutions rather than when they are directly controlled by executive branch of the government (and consequently under political influence). You can read about all the benefits of central bank independence in this ECB working paper, but as a non-economists you can view it analogously to courts independence. You want law to be administered by experts in impartial manner that will help society run more efficiently than political courts and similarly independent monetary policy helps more efficient management of money supply and other things that are under purview of monetary policy.
Having central bank and rest of the government operate at arms length, like increasing money supply through purchase of bonds, or by not even buying bonds directly at primary market but only at secondary market helps to build a wall between government and central bank.