State space may not contain all states when there are zeros in the matrix entries

In the following example, there are three inputs passed along to io_preprocessing which in turn calls structural_simplify. All three inputs are present as states in the system upon calling io_preprocessing. Before markio! is called within structural_simplify, one of the inputs, (model₊input₊u(t))[2] has been removed from fullvars, leading to the error below:

ERROR: Some specified inputs were not found in system. The following Dict indicates the found variables
Dict{Num, Bool}(
    u(t) => 1,
    (model₊input₊u(t))[2] => 0,
    d(t) => 1
)
Stacktrace:
 [1] error(::String, ::Dict{Num, Bool})
   @ Base ./error.jl:44
 [2] markio!(state::TearingState{ODESystem}, inputs::Vector{Num}, outputs::Vector{Any}; check::Bool)

using ModelingToolkitStandardLibrary.Blocks
A,C = [randn(2,2) for i in 1:2]
B = [1.0 0; 0 0]
@named model = Blocks.StateSpace(A,B,C)
@named integrator = Blocks.StateSpace( [-0.001;;], [1.0;;], [1.0;;], [0.0;;])
ins = collect(model.input.u)
disturbed_input = ins[1]
@named dist_integ = ModelingToolkit.DisturbanceModel(disturbed_input, integrator)
function add_input_disturbance_(sys, dist::DisturbanceModel, inputs)
    t = ModelingToolkit.get_iv(sys)
    @variables d(t)=0 [disturbance = true]
    @variables u(t)=0 [input = true] # Potential new system input
    dsys = ModelingToolkit.get_disturbance_system(dist)
    all_inputs = inputs
    all_inputs = Base.setindex(all_inputs, u, findfirst(isequal(dist.input), inputs)) # The input where the disturbance acts is no longer an input, the new 
    eqs = [dsys.input.u[1] ~ d
           dist.input ~ u + dsys.output.u[1]]
    augmented_sys = ODESystem(eqs, t, systems = [sys, dsys], name = gensym(:outer))

    ModelingToolkit.generate_control_function(augmented_sys, all_inputs, [d])
end

add_input_disturbance_(model, dist_integ, ins)

Start with the supplied reproduction and trace io_preprocessing into structural_simplify, especially the markio! call and the handling of fullvars. Verify that inputs corresponding to zero entries in the matrix remain available after preprocessing, and rerun the example to confirm all three inputs are found without the reported error.