It's not flat shoes that will give you problems, it's high heels. Avoid them at all costs, they are evil. They will ruin your feet, knees, hips and back. If flats were bad then all men would have foot problems. Try and find a man that has had bunions. Very rare compared to the number of women that have them because of their shoes.
I don't really know if your arches will get week, but good supportive shoes are a must for me.
The ballet flats that are popular now are very bad for your feet. They are like walking barefoot because they have absolutely NO support or cushion in them. I have learned a little heel on a shoe, like a half inch to an inch is good because it absorbs the impact of the body hitting the floor when we walk.
When I buy shoes I buy good quality, supportive, shoes with some cushion and a little bit of a heel.