It seems to me that, while understandable from a political and humanitarian view, it was arguably better strategically for Gandalf and the Rohirrim to
not go to Minas Tirith but to rather demonstrate perhaps as far as Anorien and then to gradually withdraw in a slow, fighting, scorched-earth type pullback.
The overall point of Gandalf's strategy was to distract Sauron. With Aragorn's defeating of the Corsairs and clearing South Gondor (which Gandalf knew was Aragorn's immediate goal), even with the fall of Minas Tirith there would have been strong forces opposing Sauron to the northwest and southwest. And I believe it says somewhere in LOTR there were escape routes from M.T. into the White Mountains, so some M.T. forces could have escaped to link up in South Gondor or Rohan. Such a policy would have distracted Sauron for a long time, emptied Mordor of fighters, and drawn them even further from Mordor.
Of course, there would be certain negative effects, greater devastation in Gondor and Rohan, and Sam and Frodo would presumably have been toast after fulfilling the quest
but the overall chances of success would seem to have been greater.
As for Rohan's arguably not fulfilling its alliance with Gondor, if the above policy was followed there might well have been a better chance of the overall state of Gondor surviving, and to not follow the more sound strategy would have been an error like that featured in
The Homecoming of Beorhnoth, Beorhthelm's Son.