Just to be clear, the reason they behave differently is that sqrt is an ordinary function name while √ is a unary operator.
That means, for example, that you can apply √ without parentheses:
julia> √2
1.4142135623730951
and like all operators in Julia it is “vectorized” by putting a . before the operator (a convention adopted from Matlab):
julia> .√[4,9]
2-element Vector{Float64}:
2.0
3.0
I agree with @mbauman that, if you use a binary/unary operator OP with parens, as OP(...), then it would not be crazy to allow OP.(...) as an alternative vectorization syntax similar to ordinary functions. This doesn’t seem like it would be breaking since it is currently a syntax error.