why are there no psychology apprenticeships?

When it comes to Apprenticeships, they are created if there is a demand in their respective industry for more applicants or the upskilling of existing workforces. The ones you listed are quite specialised fields and therefore most likely rely on other paths of entry, such as a formal degree. As you must keep in mind that Apprenticeships are to help people get into jobs; at least two of the three fields you mentioned are as I said quite specialised (and likely quite competitive).

I don't know how much these will help, but here you go: