Unfortunately it's the system which is broken. As a Reception teacher, I made 4 referrals last years for speech and language. We made provisions where we could in school (extra visuals etc) for those with processing issues but I find it harder with children who have speech production issues to know what to do. I'm a teacher, not a speech and language therapist. Those children are finally 'in the system', and receiving support from the speech and language therapist linked to our school, 12 months on at the start of Year 1. It took 9 months for them to be approved. It's shocking how little 'support' this actually entitles them to though. Years back, they use to come in once every 2 weeks to work with these children. Now it seems to be once a half term, which is nowhere near enough.
Once upon a time, the speech and language therapist would liase well with class TAs, having regular meetings with them and giving them targets to work on and resources to support with this, which would be copied and sent home for parents to work on daily too. Now the class teacher just gets an occasional email (twice a year?), stating targets and some suggested ideas to help (we're no longer given resources), which we then need to pass on to the TA who is to work on this child's targets with them and the S&L therapist cc's in the parent so they gave the same information. I appreciate this could be area dependent, but this is my current experience with speech and language in schools.
This year, I have 2 children who are already in the system before they started with us (like your daughter) and another 2 I am about to refer. We are yet to hear anything from the speech and language team about the ones already in the system, they are yet to visit despite them being in school for 7 weeks already now. We are chasing this, but I have no idea of their specific targets. Aybe this is what the teacher means by needing to do their own assessment? Maybe they are trying to establish what areas she needs specific support in, due to a lack of support thus far from outside agencies?
Those children I am about to refer, I sadly don't expect to be accepted for S&L support before Year 1 now (based on last year's experience of the current system).
I am so sorry you have these genuine concerns about how your daughter is being supported in school, but it's not necessarily the school's fault. Funding for all these sort of needs is at an all time low. By all means bring it up, but please don't go in all guns blazing complaining, as some are suggesting, as it's not necessarily their fault. There's only so much teachers can do to help with S&L without further guidance from those professionally trained in this area.
The use of wordless books is quite common at the start of Reception, regardless of a S&L need or not. Without the pressure of words to read, it will encourage her to talk about the pictures which tell the story in her own words. This definitely supports speaking more than decoding CVC words. They are completely different skills. So in that sense it sounds like they are supporting her needs appropriately. She'll receive books with words when she's ready, after lots of interventions to support her oral blending skills.
I sincerely hope things improve soon in terms of the support she is given, but I can only share my own experience in my own area where S&L provisions are so much poorer than they use to be :-(