Lightning has definitely struck me twice!
Last year, I wanted to hang a ceiling fan in a family room (two-story house). I carefully "stud-finded" to be sure I was between joists before cutting the sheetrock, only to find out the stud finders won't spot cross bracing and sure enough I had a cross brace just above my hole, causing me to have to cut another sheetrock hole (and patch the previous one) as the cross brace wouldn't allow space for the elec. box that would hold the fan.
Today, in the kitchen, deja vu. Freakin' cross brace just above the hole for the elec. box. *This* time, I can't get away with cuttng another hole as it'll be painfully off-center with the rest of the ceiling. Sooo, I'm thinking of reaching up in that hole and cutting out one section of the cross brace.
It won't make the house fall down, that's for sure. The cross bracing enables each joist to "share" its load with adjacent joists and therefore significantly reduces the bounce or deflection in the individual members.
Why not go for a pancake box to reduce or eliminate the need to remove important framing? Box fill can be an issue with them but I'd prefer the pancake box as a trade-off instead of removing bridging.