I see where you are coming from on this and some of the regulation is difficult to follow.
An Integrated CPL/IR course is an ab-initio course and requires no pilot qualification and staff are appointed accordingly, the fact that a proportion of students might already hold a licence has no bearing on the matter, its still an ab-initio course for the issue of a CPL.
(a) General. A person shall only carry out:
(1) flight instruction in aircraft when he/she holds:
(i) a pilot licence issued or accepted in accordance with this Regulation;
(ii) an instructor certificate appropriate to the instruction given, issued in accordance with this Subpart;
FCL.905.FI FI – Privileges and conditions
Regulation (EU) 2020/359
The privileges of FIs are to conduct flight instruction for the issue, revalidation or renewal of:
(e) a CPL in the appropriate aircraft category, provided that FIs have completed at least 200 hours of flight instruction in that aircraft category;
An Integrated ATPL/CPL course falls under the privileges stated above.
The MPL Course is a relatively new idea however; the requirements don't quite add up. It appears as though an IRI may give instruction on an Integrated MPL Course in the basic phase, but this is all conducted in simulators and you would need to meet the Multi Engine requirement for an IRI not the SE requirement.
(3) In the case of IRI already qualified to instruct on ATP(A) or CPL(A)/IR integrated courses, the requirement of (b)(2) may be replaced by the completion of the course provided for in paragraph FCL.905.FI(j)(3)."
But, there is no
FCL.905.FI(j)(3) it stops at (2) it could be (k)(3) but all reference is to FIs.
FCL.905,FI (k)(3) in the case of FIs already qualified to instruct on ATP(A) or CPL(A)/IR integrated courses, the requirement in point (2)(ii) may be replaced by the completion of a structured course of training consisting of:
(i) MCC qualification;
(ii) observation of five sessions of flight instruction in Phase 3 of an MPL course;
(iii) observation of five sessions of flight instruction in Phase 4 of an MPL course;
(iv) observation of five operator recurrent line-oriented flight training sessions;
(v) the content of the MCCI course.
In this case, FIs shall conduct their first five instructor sessions under the supervision of a TRI(A), an MCCI(A) or an SFI(A) qualified for MPL flight instruction.
As an IRI is not qualified to instruct on an ab-initio course, how anyone could become already qualified is a mystery except perhaps on a MPL Course.
I am still unable to find any legislation where it states, an IR-I can not teach candidates who are not holding other licenses than a solo-permit (which in my humble opinion is considered some type of a "license"/"rating"
Solo flying is conducted under an Exemption not to require a licence under specified conditions FCL020.
An IRI can only instruct for a rating which can only be added to a licence.