I think it's better to translate the first sentence as "We arrived late."
I sort of both agree with you and with the choice of "We are late" as an idomatic english way of describing the situation --- but definitely when I focus on the 到 in 迟到 as meaning "arrive", the perfective 了 makes more sense.
Yeah, with the English in present tense and describing a current situation, it doesn't seem right to use 了.