The problem is that this encourages (forces?) users to implement methods like Base.tryparse(::Type{Vector{Float64}}, x::String), which is piracy.
Now, most likely, this will not cause issues, since users will only implement them if they find the methods to not exist in Base. However

• It makes depdendents of Comonicon risky to use together, since different packages may define the same tryparse methods
• These methods may be implemented in future versions of Julia

A straightforward solution would be to have a distinct function like Comonicon.try_parse_arg, which has a default definition try_parse_arg(x::Type{T}, s::AbstractString) where T = tryparse(T, s).
This should not cause breakage.