Soundgarden and Alice in Chains will also get nods pretty quickly. Maybe Temple of the Dog, but they are kind of limited by having only one album. Of those Soundgarden will be the first to become eligible. I wouldn't be surprised to see Rage Against the Machine in there too. They were certainly originators in the rap/metal mashup.
Nomination is based on sales and name recognition and then on impact/influence.
The Ramones got a lot of bands to join in and it was Iggy & The Stooges that got the NYC scene started (at least as told in the book Please Kill Me, people had to wait about a year at a time for Iggy to come to town so the New York Dolls and others got into it).
Without Poison 13 and Mudhoney, there is no Pearl Jam and so also goes the grunge movement but it is unlikely that either band will get inducted. Pearl Jam does acknowledge their origins though and a hybrid band (Monkeywrench) that features members of Poison 13 and Mudhoney opened for Pearl Jam for 2 nights at Wembley.