Type inconsistencies with FFTW?

FFTW plans are <:AbstractFFTs.Plan{T} with T complex for complex-to-real plans and T real for real-to-complex plans. So the parametric type of the plan is the type of the input. However, the plans here always seem to be <:AbstractFFTs.Plan{Complex}. Is that on purpose?

julia> generic_plan = GenericFFT.plan_rfft(zeros(Float16,64))
GenericFFT.DummyrFFTPlan{ComplexF16, false, UnitRange{Int64}}(64, 1:1, #undef)

julia> fftw_plan = FFTW.plan_rfft(zeros(64))
FFTW real-to-complex plan for 64-element array of Float64
(rdft2-ct-dit/8
  (hc2c-direct-8/28/1 "hc2cfdftv_8_avx2"
    (rdft2-r2hc-direct-8 "r2cf_8")
    (rdft2-r2hc01-direct-8 "r2cfII_8"))
  (dft-direct-8-x4 "n2fv_8_avx2_128"))

julia> supertype(supertype(typeof(fftw_plan)))
AbstractFFTs.Plan{Float64}

julia> supertype(supertype(typeof(generic_plan)))
AbstractFFTs.Plan{ComplexF16}     # expected Float16 not ComplexF16

Reproduce the examples using GenericFFT.plan_rfft and FFTW.plan_rfft, then inspect the resulting AbstractFFTs.Plan type parameters. The work is done when real-to-complex and complex-to-real plans report the same input-type parameter convention as FFTW without breaking the demonstrated plan construction.