Is it sensible to think that time is more fundamental than space, because one can just close one's eyes and relive memories, going back in time or prospectively go forward in time to predict something, without actually changing your position in space?

Our experience of objects (including ourselves) in space and time seems vital to our human existence, and I'm not sure what it would mean to say that either spatiality or temporality is more important than the other. Since thinking about events that may have happened in the past or events is not literally time travel, so spatiality seems to "beat" temporality with respect to ease of travel, which your question refers to. The difficulty of self-directed travel through time doesn't mean that temporality is unimportant, however.