Question: Mapping arithmetic operators onto equations: Why don't they work the same way

eqs := [a = b, c = d, e = f]:

map(`+`, eqs, 2);
map(`-`, eqs, 2);
map(`/`, eqs, 2);
         [a + 2 = b + 2, c + 2 = d + 2, e + 2 = f + 2]

         [a - 2 = b - 2, c - 2 = d - 2, e - 2 = f - 2]

               [1     1    1     1    1     1  ]
               [- a = - b, - c = - d, - e = - f]
               [2     2    2     2    2     2  ]

These work differently

map(`*`, eqs, 2);
map(`^`, eqs, 2);
               [2 (a = b), 2 (c = d), 2 (e = f)]

Error, non-algebraic base in a power: a = b

(The first one can be dealt with by applying eval to the output)

Why do not all work the same way?

Edit:
Generic work arounds where arithop is one of: + - / * ^

map(eval@`arithop`, eqs, 2);
map(map@`arithop`, eqs, 2);# Update: Maple 2021 and higher
[seq(i arithop 2, i in eqs)];