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This is indeed a misdesign of the limit wrapper method/function. Feel free to propose an enhancement.

Workarounds :

sage: X=var("x", n=3)
sage: f=sum(X) ; f
x0 + x1 + x2
sage: f.maxima_methods().limit(X[0], 1)
x1 + x2 + 1
sage: maxima_calculus.limit(f, X[0], 1)._sage_()
x1 + x2 + 1
sage: from sympy import sympify
sage: f._sympy_().limit(*map(sympify, (X[0], 1)))._sage_()
x1 + x2 + 1

HTH,