Is this 全くだ meant to be irony?

Question

「あそこで雪像作ってるのに混じってきたらどうですか？」

【湯花】「肉体労働とかあり得ないわー。学園の除雪だって面倒だから課外授業の一環として生徒にさせてるのに」

「思ってても言うべきじゃない事ってありますよね、特に大人は」

【湯花】「全くだ」

In the above extract, 湯花, said 全くだ in agreement with what the other character said. Her previous statement is not exactly in line with this idea. Is this meant to be ironic or am I missing something?

Answer 1

Though I'm ignorant of the preceding setting, Yuhana declined the other character’s suggestion for Yuhana to join the production work of snow statues by adding an unnecessary and problematic reasoning – the teachers are letting their pupils engage in heavy work of removing accumulated snow from the schoolhouse because it’s troublesome for teachers to do it.

The other one hanged on this remark of Yuhana, and warned her not to say such an insensible thing – to let school children clear the snow, even she envisaged so.

Yuhana responded “It’s true, exactly” in realization of, and remorse for that her own remark – letting pupils engage in heavy labor of clearing snow as a part of extracurricular activities was thoughtless.

So, Yuhana’s 「全くだ」is not an irony, nor it does contradict with preceding passage. It’s Yuhana’s self-reflection for admitting her reference to letting school children clear snow was inappropriate rational for her not willing to join the snow work as well as a remark to be made by an adult. She admits it's her gaffe.

Answer 2

I feel this depends on the context and her character.

• (most likely) 湯花 was talking to her close friend, and she wanted to confess her feelings anyway, knowing it was not suitable. (全くだ ≒ Yeah, I know) (Can I say she's being ironical?)
• (less likely) 湯花 changed her mind after the other person pointed out it was not suitable. (全くだ ≒ Fine, you're right.)
• (possible) 湯花 is an お調子者 character, and said 全くだ purely as a joke (ボケ).