ldiv for PseudoBlockMatrix two times slower than for native Matrix

PseudoBlockMatrix is a structured wrapper to a native array. This is why the following came as a surprise:

using BlockArrays

n = 800
M = rand(2n,2n)
v = rand(2n)

pbM = PseudoBlockMatrix(M,[n,n],[n,n])
pbv = PseudoBlockVector(v,[n,n])

using BlockArrays.ArrayLayouts

MemoryLayout(M) == MemoryLayout(pbM)
MemoryLayout(v) == MemoryLayout(pbv)

@time u = M \ v;
@time pbu = pbM \ pbv;

output:

0.053086 seconds (4 allocations: 19.556 MiB, 9.18% gc time)
0.126742 seconds (19 allocations: 39.992 MiB, 2.13% gc time)

For matrices of larger size it remains true that solving the system with BlockPseudoArrays is two times slower. Where could this originate from?

Reproduce the benchmark from the issue using native Matrix and PseudoBlockMatrix with the \ operator, then compare allocations and timings. Trace the PseudoBlockMatrix solve path and its MemoryLayout handling to locate the slowdown; done means identifying the cause and demonstrating improved performance against the native case.