Don't count on the photos turning out well just because there will be people with phones at the party. When you're in host mode, worrying about whether the kids are eating, whether they're bored, whether anyone's fighting, you basically don't have time to photograph anything. And the guests even less so: they're socializing, not documenting.
The real issue with €250 is asking yourself whether you actually want those photos afterward. Here's what others don't mention: you need to be sure the photographer understands what you're looking for. With 7-year-olds it can happen that she spends her time taking very posed, very formal photos, when what you probably want are natural moments, laughter, the controlled chaos of a party. Ask her for examples of previous work at children's parties, not just studio sessions. If her photos show kids too organized looking at the camera, maybe she's not the right fit.
That said, €250 for 3 hours is what it costs to try to do it right. The phone photos everyone else takes will probably end up lost in unnamed folders in five years. A professional photographer delivers them edited, organized, backed up. That has value if you choose well. If the budget's really tight, it might be reasonable not to do it, but not because "we all have phones" - that's exactly why it makes sense to hire someone who does this for a living.