Tidally locked planet - shouldn't the Goldilocks zone be wider?

[halfelven]

Okay, so planets in the Goldilocks zone are far enough from the star that it's less likely they are tidally locked. But assuming such a thing exists - shouldn't the habitable zone be wider if the planet is tidally locked to its star?

At one extreme, the planet would have an Antarctica-sized area with liquid water under the bright spot, and frozen solid everywhere else; that should be enough to sustain life. At the other extreme, there would be a mild temperate area on the dark spot, and a steamy inferno everywhere else.

It seems to me these extremes would correspond to an orbital zone wider than the one required by fast-spinning planets. Is my intuition wrong?

 

[fructivore]

It seems like your scenario assumes that you are both tidally locked -and- have an axial tilt close to zero.

If your planet is tilted, on the other hand, you would have seasonal variations in your temperature patterns, which might actually be more conducive to life, as it would seem to encourage more of a "mixing" effect.

There is something compelling about the idea of life or even civilization evolving in the warm zone of a world otherwise in the grip of a perpetual ice age.