You are correct that the gain in the year of the sale would be the same regardless if they took depreciation or not.  Maybe we misunderstood your original question.

But the long-term would be more tax due to not taking depreciation (missed deductions in prior years), so it is dumb to not take depreciation.

However, it is possible that missed depreciation in prior years could result in higher tax in the year of the sale.  Rentals often have passive losses that are not allowed.  Those losses often carry forward and may not be usable until the property is sold.  If you missed some prior depreciation, the passive loss carryforward will be smaller, resulting in more tax in the year it is sold.