Goku would just destroy the entirety of the shinigami and human realms.

Ummmmmm..........u forgor u need to touch them to do so

Goku cannot defeat Ryuk since there is no countermeasure to the Death Note. The best thing that can be done is to get hold of Ryuk's Death Note. As long as the Death Note remains with Goku, Ryuk will not hurt him. Writing down Ryuk's name in the Death Note will also do no good since he is a shinigami.

As a Shinigami, Ryuk has a distinct advantage against those living in the mortal realm. There seem to be few limits to his ability to harvest souls, so despite Goku's overwhelming strength, the Saiyan would presumably be helpless to stop Ryuk if the Shinigami decided to claim his life.2

But you forgot the death note only works on humans and Goku is not human

Whhhhhhhhaaaaaaat ig u forgor it works on "mortals" which means who can die and thus Goku can he will be affected by Death note

But Goku after dying just receives a halo and still could fight

Then what's the point if he dies

He could still fight him

First of watch death note the only way to kill a god of death is to by letting him save a human's life so basically Goku has to seduce Ryuk

He did a few gods his friends so

So u think he call make ryuk fall in love so that ryuk write's someone name in death note

i'd hate to break it to you but, naruto with kurama could defeat him