The UK was already a member of the EEA, ok it was by virtue of it's EU membership in the end, but the UK was a founder member. If the UK had decided that it wanted to maintain it when it left the EU I can't imagine who would have objected?
From what people were saying at the time, the other EEA-but-not-EU members didn’t much like the idea of their group being dominated by the UK.
I have no insight into how significant that concern would have been in practice, only that it reached the news.