The key is that they are SEPARATE licences
Not sure how this ties in with the relevant wording of the Aircrew Regulation:
FCL.015 Application and issue of licences, ratings and certificates
(a) [...]
(b) [...]
(c) A person shall not hold at any time more than one licence per category of aircraft issued in accordance with this Part.
Elsewhere, the Regulation states:
FCL.305 CPL — Privileges and conditions
(a) Privileges. The privileges of the holder of a CPL are, within the appropriate aircraft category, to:
(1) exercise all the privileges of the holder of an LAPL and a PPL;
And for the ATPL:
FCL.505 ATPL — Privileges
(a) The privileges of the holder of an ATPL are, within the appropriate aircraft category, to:
(1) exercise all the privileges of the holder of an LAPL, a PPL and a CPL;