My DS-now-7 had a similar phase at around the same age. TBH it never occurred to me to try to push him through it - I just assumed it would pass, and indeed it did. I think it lasted a year or so, during which time he read a lot of non-fiction and a lot of fiction he'd had for a long time, but very little fiction that was new to him. (And then he went quite the other way, and he was perfectly happy reading Harry Potter and other stuff I had found quite scary!)
I think it might be useful to separate the issue into two: you mention both being concerned about your DD's limiting herself, and your own feeling of it being boring to read to her. Here's my 2pworth just to consider; YMMV.
- I think it's quite reasonable, with a child who can read to herself, not to be willing to give her a free choice of what you read. If she wants something you're sick of she can read it to herself, and that's absolutely fine. This may be harder to negotiate if for you reading is an everyday-ritual thing, but we slipped into reading being sporadic and only when we both felt like it once DS could really read to himself, and it seems to have worked for us. (We still read aloud to him sometimes, so in our case it wasn't a decision that led to not reading aloud at all.)
- I suppose that if I thought my child would still be shying away from even minimally scary fiction several years later, I'd worry about that, but I somehow just assumed it would be a phase and so it proved for my DS. As I said it didn't occur to me to push him through it; maybe part of the reason was that I felt I recognised the feeling. E.g. I'm into crime fiction, but there have been years of my life - especially when I had a baby/toddler and after my DH nearly died - when I went completely off it. I just didn't want to go there, it wasn't fun. I suppose I assumed that something about DS's development was putting him into a similar mindset. I'd certainly have given short shrift to anyone who told me I ought to get back to reading crime novels when I didn't feel like it! For me this comes under "recognise and respect one's own feelings" which is something I want to encourage (in both myself and DS!)
Concretely, I suppose I also wouldn't have wanted him thinking about things he found scary at bedtime.
I realise that's pretty opinionated; I'm sure it was right for my family, but let me reiterate that YMMV. It may well be closely connected with personality factors - I've always reacted badly to being pushed into doing things "because you'll love it really" and similarly wouldn't do that to DS, but I see that for some other people that does work out for the best.
