If you have never held a licence other than an MPL, you will never have demonstrated your ability to fly a single-pilot aeroplane and, consequently, you ATPL(A) will be restricted to multi-pilot operations only. In order to remove the restriction, you will need to have complied with the experience and training requirements detailed in FCL.325.A and to have passed the CPL skill test and the IR skill test in a single-pilot aeroplane. However, if you have previously held any licence other than a MPL (i.e. LAPL, PPL or CPL) then the ATPL should be issued without the restriction. What is not clear is why you should have to pass the CPL skill test to remove the restriction when a previously held LAPL is sufficient to prevent the licence being restricted in the first place.
It is not true to say that all ATPLs are restricted to multi-pilot operations - it's the other way around. You cannot act as PIC of a multi-pilot aeroplane unless you hold an ATPL but the privileges of an ATPL (except if restricted as above) include the privileges of a CPL, PPL and LAPL.